chapter 4 resource masters - loudoun county 8... · chapter 4 test, form 3 ... chapter 4 resource...

Course 1

Chapter 4Resource Masters

Course 3

Chapter 4Resource Masters

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce thematerial contained herein on the condition that such material be reproduced only forclassroom use; be provided to students, teacher, and families without charge; andbe used solely in conjunction with Glencoe Mathematics: Applications andConcepts, Course 3. Any other reproduction, for use or sale, is prohibited withoutprior written permission of the publisher.

Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240

Mathematics: Applications and Concepts, Course 3ISBN: 0-07-860147-9 Chapter 4 Resource Masters

1 2 3 4 5 6 7 8 9 10 024 12 11 10 09 08 07 06 05 04 03

Consumable Workbooks

Many of the worksheets contained in the Chapter Resource Mastersbooklets are available as consumable workbooks in both English andSpanish.

Study Guide and Intervention Workbook 0-07-860162-2

Study Guide and Intervention Workbook (Spanish) 0-07-860168-1

Practice: Skills Workbook 0-07-860163-0

Practice: Skills Workbook (Spanish) 0-07-860169-X

Practice: Word Problems Workbook 0-07-860164-9

Practice: Word Problems Workbook (Spanish) 0-07-860170-3

Reading to Learn Mathematics Workbook 0-07-861062-1

Answers for Workbooks The answers for Chapter 4 of theseworkbooks can be found in the back of this Chapter Resource Mastersbooklet.

Spanish Assessment Masters Spanish versions of forms 2A and 2C ofthe Chapter 4 Test are available in the Glencoe Mathematics: Applicationsand Concepts Spanish Assessment Masters, Course 3 (0-07-860172-X).

iii

Vocabulary Builder .............................vii

Family Letter............................................ix

Family Activity ........................................x

Lesson 4-1Study Guide and Intervention ........................185Practice: Skills ................................................186Practice: Word Problems................................187Reading to Learn Mathematics......................188Enrichment .....................................................189








Chapter 4 AssessmentChapter 4 Test, Form 1 ..........................225–226Chapter 4 Test, Form 2A........................227–228Chapter 4 Test, Form 2B........................229–230Chapter 4 Test, Form 2C........................231–232Chapter 4 Test, Form 2D........................233–234Chapter 4 Test, Form 3 ..........................235–236Chapter 4 Extended Response Assessment .237Chapter 4 Vocabulary Test/Review.................238Chapter 4 Quizzes 1 & 2................................239Chapter 4 Quizzes 3 & 4................................240Chapter 4 Mid-Chapter Test ...........................241Chapter 4 Cumulative Review........................242Chapter 4 Standardized Test Practice....243–244

Standardized Test Practice Student Recording Sheet ..............................A1

Standardized Test Practice Rubric...................A2ANSWERS .............................................A3–A32

CONTENTS

iv

Teacher’s Guide to Using the Chapter 4 Resource Masters

The Fast File Chapter Resource system allows you to conveniently file the resources youuse most often. The Chapter 4 Resource Masters includes the core materials needed forChapter 4. These materials include worksheets, extensions, and assessment options. Theanswers for these pages appear at the back of this booklet.

All of the materials found in this booklet are included for viewing and printing in theGlencoe Mathematics: Applications and Concepts, Course 3, TeacherWorks CD-ROM.

Vocabulary Builder Pages vii-viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.

When to Use Give these pages to studentsbefore beginning Lesson 4-1. Encouragethem to add these pages to theirmathematics study notebook. Remind themto add definitions and examples as theycomplete each lesson.

Family Letter and Family ActivityPage ix is a letter to inform your students’families of the requirements of the chapter.The family activity on page x helps themunderstand how the mathematics studentsare learning is applicable to real life.

When to Use Give these pages to studentsto take home before beginning the chapter.

Study Guide and InterventionThere is one Study Guide and Interventionmaster for each lesson in Chapter 4.

When to Use Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.

Practice: Skills There is one master foreach lesson. These provide practice thatmore closely follows the structure of thePractice and Applications section of theStudent Edition exercises.

When to Use These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.

Practice: Word Problems There is onemaster for each lesson. These providepractice in solving word problems that applythe concepts of the lesson.

When to Use These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.

Reading to Learn Mathematics Onemaster is included for each lesson. The firstsection of each master asks questions aboutthe opening paragraph of the lesson in theStudent Edition. Additional questions askstudents to interpret the context of andrelationships among terms in the lesson.Finally, students are asked to summarizewhat they have learned using variousrepresentation techniques.

When to Use This master can be used as astudy tool when presenting the lesson or asan informal reading assessment afterpresenting the lesson. It is also a helpful toolfor ELL (English Language Learner)students.

v

Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.

When to Use These may be used as extracredit, short-term projects, or as activitiesfor days when class periods are shortened.

Assessment OptionsThe assessment masters in the Chapter 4Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.

Chapter AssessmentChapter Tests

• Form 1 contains multiple-choice questionsand is intended for use with basic levelstudents.

• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.

• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.

• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.

All of the above tests include a free-responseBonus question.

• The Extended-Response Assessmentincludes performance assessment tasksthat are suitable for all students. Ascoring rubric is included for evaluationguidelines. Sample answers are providedfor assessment.

• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used inconjunction with one of the chapter testsor as a review worksheet.

Intermediate Assessment• Four free-response quizzes are included

to offer assessment at appropriateintervals in the chapter.

• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice and free-response questions.

Continuing Assessment• The Cumulative Review provides

students an opportunity to reinforce andretain skills as they proceed through theirstudy of Glencoe Mathematics:Applications and Concepts, Course 3. Itcan also be used as a test. This masterincludes free-response questions.

• The Standardized Test Practice offerscontinuing review of pre-algebra conceptsin various formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, short response, grid-in, andextended response questions. Bubble-inand grid-in answer sections are providedon the master.

Answers• Page A1 is an answer sheet for the

Standardized Test Practice questions thatappear in the Student Edition on pages 202–203. This improves students’familiarity with the answer formats theymay encounter in test taking.

• Detailed rubrics for assessing theextended response questions on page 203are provided on page A2.

• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.

• Full-size answer keys are provided for theassessment masters in this booklet.

This is an alphabetical list of new vocabulary terms you will learn inChapter 4. As you study the chapter, complete each term’s definitionor description. Remember to add the page number where you foundthe term. Add this page to your math study notebook to reviewvocabulary at the end of the chapter.

Vo

cab

ula

ry B

uild

er

© Glencoe/McGraw-Hill vii Mathematics: Applications and Concepts, Course 3

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn MathematicsVocabulary Builder

Vocabulary TermFound

Definition/Description/Exampleon Page

congruent

corresponding parts

cross products

dilation[deye-LAY-shuhn]

indirect measurement

polygon

proportion

rate

rate of change

© Glencoe/McGraw-Hill viii Mathematics: Applications and Concepts, Course 3

Vocabulary TermFound

Definition/Description/Exampleon Page

ratio

rise

run

scale

scale drawing

scale factor

scale model

similar

slope

unit rate

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn MathematicsVocabulary Builder (continued)

© Glencoe/McGraw-Hill ix Mathematics: Applications and Concepts, Course 3

Family LetterNAME ________________________________________ DATE ______________ PERIOD _____

Dear Parent or Guardian:

“When am I ever going to use this stuff?” Students in math

classes often ask this question. Too often, math seems to be a

series of procedures that one learns and then uses to solve a

particular type of problem—without having any application to

the real world. In our math class, however, we try to take

mathematics beyond the classroom to a point where students

will realize and appreciate its importance in their daily lives.

In Chapter 4, Proportions, Algebra, and Geometry, your

child will learn about ratios, rates, and proportions. Your child

will also learn about slope as a rate of change and will find the

slope of a line. In addition, your child will learn to make scale

models and use indirect measurement. In the study of this

chapter, your child will complete a variety of daily classroom

assignments and activities and possibly produce a chapter

project.By signing this letter and returning it with your child, you agree

to encourage your child by getting involved. Enclosed is an

activity that you can do with your child that also relates the

math we will be learning in Chapter 4 to the real world. You

may also wish to log on to the Online Study Tools for self-

check quizzes, Parent and Student Study Guide pages, and

other study help at www.msmath3.net. If you have any

questions or comments, feel free to contact me at school.

Sincerely,

Fam

ily L

ette

r

Signature of Parent or Guardian ______________________________________ Date ________

© Glencoe/McGraw-Hill x Mathematics: Applications and Concepts, Course 3

Family ActivityNAME ________________________________________ DATE ______________ PERIOD _____

Scale Drawings and ModelsWork with a family member. Below is a scale drawing of a house plan. Thescale for the drawing is �

12� inch � 3 feet. Use the drawing to answer the

following questions. You will need a ruler to complete this activity.

1. What are the dimensions of the kitchen in the drawing?

2. What are the dimensions of the kitchen in real life?

3. What is the area of Bedroom 2 in the drawing?

4. What is the area of Bedroom 2 in real life?

5. How many square feet of carpet will be needed to carpet the living roomand the hallway?

1.2�14

�in.by 1�12

�in.2.13�12

�ft by 9 ft3.3 in24.108 ft25.310�12

�ft2

Bedroom 2

Bath Bedroom 1

Bedroom 3 Kitchen

Living Room

Less

on

4–1

© Glencoe/McGraw-Hill 185 Mathematics: Applications and Concepts, Course 3

Express 35 wins to 42 losses in simplest form.

�3452�

� �56� Divide the numerator and denominator by the greatest common factor, 7.

The ratio in simplest form is �56� or 5:6.

Express 1 foot to 3 inches in simplest form.

To simplify a ratio involving measurements, both quantities must have the same unitof measure.

�31in

fcohotes� � �

132

iinncchheess

� Convert 1 foot to 12 inches.

� �41ininchch

es� Divide the numerator and denominator by 3.

The ratio in simplest form is �41� or 4:1.

Express 309 miles in 6 hours as a unit rate.

�3609

homuirless

� � �51

1.5

hmou

irles

� Divide the numerator and denominator by 6 to get a denominator of 1.

The unit rate is 51.5 miles per hour.

Express each ratio in simplest form.

1. 3 out of 9 students 2. 8 passengers:2 cars

3. 5 out of 10 dentists 4. 35 boys:60 girls

5. 18 red apples to 42 green apples 6. 50 millimeters to 1 meter

Express each rate as a unit rate.

7. 12 waves in 2 hours 8. 200 miles in 4 hours

9. 21 gallons in 2.4 minutes 10. $12 for 4.8 pounds

11. $49,500 in 12 months 12. 112 feet in 5 seconds

A rate is a ratio that compares two quanitities with different types of units. A unit rate is a rate with adenominator of 1.

A ratio is a comparison of two numbers by division. Since a ratio can be written as a fraction, it can be simplified.

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionRatios and Rates



1. 15 cats:50 dogs 2. 18 adults to 27 teens

3. 27 nurses to 9 doctors 4. 12 losses in 32 games

5. 50 centimeters:1 meter 6. 1 foot:1 yard

7. 22 players:2 teams 8. $28:8 pounds

9. 8 completions:12 passes 10. 21 hired out of 105 applicants

11. 18 hours out of 1 day 12. 64 boys to 66 girls

13. 66 miles on 4 gallons 14. 48 wins:18 losses

15. 112 peanuts:28 cashews 16. 273 miles in 6 hours


17. 96 students in 3 buses 18. $9,650 for 100 shares of stock

19. $21.45 for 13 gallons of gasoline 20. 125 meters in 10 seconds

21. 30.4 pounds of tofu in 8 weeks 22. 6.5 inches of rainfall in 13 days

23. 103.68 miles in 7.2 hours 24. $94.99 for 7 pizzas

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: SkillsRatios and Rates


Practice: Word ProblemsRatios and Rates

NAME ________________________________________ DATE ______________ PERIOD _____

Less

on

4–1

1. COOKING In a bread dough recipe,there are 3 eggs for every 9 cups offlour. Express this ratio in simplestform.

2. WILDLIFE Dena counted 14 robins out of150 birds. Express this ratio insimplest form.

3. INVESTMENTS Josh earned dividends of$2.16 on 54 shares of stock. Find thedividends per share.

4. TRANSPORTATION When Denise boughtgasoline, she paid $18.48 for 11.2gallons. Find the price of gasoline pergallon.

5. WATER FLOW Jacob filled his 60-gallonbathtub in 5 minutes. How fast was thewater flowing?

6. TRAVEL On her vacation, Charmaine’sflight lasted 4.5 hours. She traveled954 miles. Find the average speed ofthe plane.

7. HOUSING Mr. And Mrs. Romero boughta 1,200 square-foot house for $111,600.How much did they pay per squarefoot?

8. SHOPPING A breakfast cereal comes intwo different sized packages. The8-ounce box costs $2.88, while the12-ounce box costs $3.60. Which box isthe better buy? Explain your reasoning.


Pre-Activity Read the introduction at the top of page 156 in your textbook.Write your answers below.

1. Which combination of ingredients would you use to make a smalleramount of the same recipe? Explain.

2. In order to make the same recipe of trail mix, how many scoops ofpeanuts should you use for every scoop of raisins?

Reading the Lesson3. What does it mean if the ratio of red marbles to blue marbles is 3 to 5?

4. What is another way to write the ratio 3 to 5?

5. What must you do before you can simplify the ratio 30 minutes to 8 hours? What is the simplified ratio?

Helping You Remember6. When you go to a bank to exchange money of one currency for another,

the bank uses a conversion rate to calculate the amount of money in thenew currency. Find out what the current conversion rate is to exchangeU.S. dollars to Canadian dollars at a local bank. Then write the rate as aratio of one currency compared to the other.

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn MathematicsRatios and Rates


Bargain HuntingRates are useful and meaningful when expressed as a unit rate.For example, which is the better buy—one orange for $0.29 or12 oranges for $3.00?

To find the unit rate for 12 oranges, divide $3.00 by 12. Theresult is $0.25 per orange. If a shopper needs to buy at least12 oranges, then 12 oranges for $3.00 is the better buy.

For each exercise below, rates are given in Column A and Column B. In the blank next to each exercise number, write the letter of the column that contains the better buy.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

OR

ANG

ES

EnrichmentNAME ________________________________________ DATE ______________ PERIOD _____

Less

on

4–1

Column A Column B

1 apple for $0.19 3 apples for $0.59

20 pounds of pet food for $14.99 50 pounds of pet food for $37.99

A car that travels 308 miles on11 gallons of gasoline

A car that travels 406 miles on14 gallons of gasoline

10 floppy discs for $8.99 25 floppy discs for $19.75

1-gallon can of paint for $13.99 5-gallon bucket of paint for$67.45

84 ounces of liquid detergentfor $10.64

48 ounces of liquid detergentfor $6.19

5,000 square feet of lawn foodfor $11.99

12,500 square feet of lawn foodfor $29.99

2 compact discs for $26.50 3 compact discs for $40.00

8 pencils for $0.99 12 pencils for $1.49

1,000 sheets of computer paperfor $8.95

5,000 sheets of computer paperfor $41.99


INCOME The graph shows Mr. Jackson’s annual income between 1994 and 2002.Find the rate of change in Mr. Jackson’s income between 1994 and 1997.

Use the formula for the rate of change.Let (x1, y1) � (1994, 48,500) and (x2, y2) � (1997, 53,000).

�yx

2

2

––

yx

1

1� ��

531,090907

��

4189,95400

� Write the formula for rate of change.

� �4,5

300� Simplify.

� �1,5

100� Express this rate as a unit rate.

Between 1994 and 1997, Mr. Jackson’s income increased an average of $1,500 per year.

SURF For Exercises 1–3, use the graph that shows the average daily wave height as measured by an ocean buoy over a nine-day period.

1. Find the rate of change in the average daily wave height between day 1 and day 3.



y

x

Days

7

9

11

13

15

1 3 5 7 9

Day

Wave Height

(7, 14)

(9, 11)

(3, 12)

(1, 8)

0

'94 '96 '98 '00 '02

50,000

45,000

55,000

60,000

65,000

Annu

al In

com

e ($

)

Year

Mr. Jackson's Income

y

x

1994, 48,500

2002, 57,000

1997, 53,000

0

To find the rate of change between two data points, divide the difference of the y-coordinates by the

difference of the x-coordinates. The rate of change between (x1, y1) and (x2, y2) is �xy

2

2�

� yx

1

1�.

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionRate of Change


TEMPERATURE Use the table below that shows the high temperature ofa city for the first part of August.

1. Find the rate of change in the high temperature between August 1 andAugust 5.

2. Find the rate of change in the high temperature between August 5 andAugust 14.

3. During which of these two time periods did the high temperature risefaster?

4. Find the rate of change in the high temperature between August 14 andAugust 15. Then interpret its meaning.

COMPANY GROWTH Use the graph that shows the number of employees at a company between 1994 and 2002.

5. Find the rate of change in the number of employees between 1994 and 1996.

6. Find the rate of change in the number of employees between 1996 and 1999.

7. During which of these two time periods did the number of employees grow faster?

8. Find the rate of change in the number of employees between 1999 and 2002. Then interpret its meaning.

y

x

Num

ber o

f Em

ploy

ees

10

20

30

40

50

01994 1996 1998 2000 2002

Year

Company Growth

(1999, 41)

(2002, 38)(1996, 32)

(1994, 18)

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: SkillsRate of Change

Less

on

4–2

Date 1 5 14 15

High Temperature (ºF) 85 93 102 102


ELECTIONS For Exercises 1–3, use the table that shows the total numberof people who had voted in District 5 at various times on election day.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word ProblemsRate of Change

1. Find the rate of change in the numberof voters between 8:00 A.M. and10:00 A.M. Then interpret its meaning.

2. Find the rate of change in the numberof voters between 10:00 A.M. and1:00 P.M. Then interpret its meaning.

3. During which of these two time periodsdid the number of people who hadvoted so far increase faster? Explainyour reasoning.

4. MUSIC At the end of 1999, Candace had47 CDs in her music collection. At theend of 2002, she had 134 CDs. Find therate of change in the number of CDs inCandace’s collection between 1999 and2002.

5. FITNESS In 1992, the price of an annualmembership at Mr. Jensen’s health clubwas $225. In 2002, the price of thesame membership was $319.50. Findthe rate of change in the price of theannual membership between 1992 and2002.

6. HIKING Last Saturday Fumio and Kishiwent hiking in the mountains. Whenthey started back at 2:00 P.M., theirelevation was 3,560 feet above sealevel. At 6:00 P.M., their elevation was2,390 feet. Find the rate of change oftheir elevation between 2:00 P.M. and6:00 P.M. Then interpret its meaning.

Time 8:00 A.M. 10:00 A.M. 1:00 P.M. 4:30 P.M. 7:00 P.M.

Number of Voters 141 351 798 1,008 1,753

Less

on

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1. By how many bears did Alicia’s collection increase between 1997 and1999? Between 1999 and 2002?

2. Between which years did Alicia’s collection increase the fastest?

Reading the Lesson3. What does a rate of change measure on a graph?

4. On a graph, what does it mean when a rate of change is negative?

5. Complete the sentence: When a quantity does not change over a period oftime, it is said to have a __________ rate of change.

Helping You Remember6. Write out in words the formula for finding a rate of change between two

data points (x1, y1) and (x2, y2).

Reading to Learn MathematicsRate of Change


NAME ________________________________________ DATE ______________ PERIOD _____


Analyzing GraphsA graph can be used to represent many real-life situations. Graphs such asthese often have time as the dimension on the horizontal axis. By analyzingthe rate of change of different parts of a graph, you can draw conclusionsabout what was happening in the real-life situation at that time.

TRAVEL The graph at the right represents the speedof a car as it travels along the road. Describe whatis happening in the graph.

• At the origin, the car is stopped.

• Where the line shows a fast, positive rate ofchange, the car is speeding up.

• Then the car is going at a constant speed,shown by the horizontal part of the graph.

• The car is slowing down where the graphshows a negative rate of change.

• The car stops and stays still for a short time. Then it speeds up again.The starting and stopping process repeats continually.

Analyze each graph.

1. Ashley is riding her bicycle along a scenic trail.Describe what is happening in the graph.

2. The graph shows the depth of water in a pond as youtravel out from the shore. Describe what is happening in the graph.

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment

car is acceleratingmaintaining speed

car is slowing downcar is stopped

Spee

d (

mp

h)

Time (min)0

Spee

d (

ft/s

)

Time (min)0

Dep

th (

ft)

Distance from Shore (ft)0

Less

on

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Study Guide and InterventionSlope


NAME ________________________________________ DATE ______________ PERIOD _____

Find the slope of the line in the graph.

Choose two points on the line. The vertical change from pointA to point B is 4 units while the horizontal change is 2 units.

slope � �rriusne

� Definition of slope

� �42� The rise is 4, and the run is 2.

� 2 Simplify.

The slope of the line is 2.

The points in the table lie on a line. Find the slope of the line.

slope � �rriusne

� �cchhaannggee

iinn

yx

�

� ��34� or ��

43�

The slope of the line is ��43�.

Find the slope of each line.

1. 2. 3.

The points given in each table lie on a line. Find the slope of the line.

4. 5.

y

xO

y

xO

y

xO

The slope of a line is the ratio of the rise, or vertical change, to the run, or horizontal change.

y

xO

rise: 4

run: 2

B

A

x �2 1 4 7

y 5 1 �3 �7

� � �

� � �� 3

x �5 0 5 10

y 4 3 2 1

x 3 5 7 9

y �1 2 5 8

� 3 � 3

� 4 � 4 � 4

←←

Practice: SkillsSlope



1. 2. 3.

4. 5. 6.

The points given in each table lie on a line. Find the slope of the line.Then graph the line.

7. 8. 9.

10. 11. 12.

y

xO

y

xO O

y

xO

y

xO

y

xO

y

xO

y

xO

y

xO

y

xO

y

xO

y

xO

y

xO

NAME ________________________________________ DATE ______________ PERIOD _____

x �4 �2 0 2

y 3 3 3 3

x �7 �5 �3 �1

y �6 �3 0 3

x �8 �4 0 4

y 8 5 2 �1

x �2 �1 0 1

y 2 1 0 �1

x 1 3 5 7

y 6 5 4 3

x 0 3 6 9

y 1 2 3 4

Less

on

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Practice: Word ProblemsSlope


FLOWERS For Exercises 1 and 2, use LONG DISTANCE For Exercises 3–6, use the graph that shows the depth of the the graph that compares the costs of water in a vase of flowers over 8 days. long distance phone calls with three

different companies.

NAME ________________________________________ DATE ______________ PERIOD _____

y

x0

1

1 2 3 4 5 6 7 8 9 10

23456789

10

Depth of Water in Vase

Dept

h (in

.)

Day

1. Find the slope of the line. 2. Interpret the meaning this slope as a

rate of change.

y

x0 1 2 3 4 5 6 7 8 9

0.50

1.00

1.50

2.00

2.50

Long Distance Charges

Cost

($)

Length of Call (minutes)

Company A

Company B

Company C

3. Find the slope of the line for CompanyA. Then interpret this slope as a rate ofchange.

4. Find the slope of the line for Company B. Then interpret this slope as a rate of change.

5. Find the slope of the line for CompanyC. Then interpret this slope as a rate ofchange.

6. Which company charges the least foreach additional minute? Explain yourreasoning.


1. Pick several pairs of points from those plotted and find the rate of changebetween them. Write each rate in simplest form.

2. What is true of these rates?

Reading the Lesson3. Slope can be positive, negative, or zero. For each one of these possibilities

draw an example of a line with that kind of slope.

Helping You Remember4. The slope of a line is defined by the rise compared to the run between any

two points on the line. Think about the words rise and run. How can youremember which word represents vertical change and which wordrepresents horizontal change?

y

xO

y

xO

y

xO

Reading to Learn MathematicsSlope


NAME ________________________________________ DATE ______________ PERIOD _____

Less

on

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Chien-Shiung WuAmerican physicist Chien-Shiung Wu (1912–1997) was born in Shanghai, China. In 1936, she came to the United States to further her studies in science. She received her doctorate in physics in 1940 from the University of California, and became known as one of the world’s leading physicists. In 1975, she was awarded the National Medal of Science.

Wu is most famous for an experiment that she conducted in 1957. The outcome of the experiment was considered the most significant discovery in physics in more than seventy years. The exercise below will help you learn some facts about it.

The points given in each table lie on a line. Find the slope of the line.The word or phrase following the solution will complete thestatement correctly.

1. 2.

At the time of the experiment, Wu The site of the experiment was the was a professor at . in Washington, D.C.slope � 3: Columbia University slope � 0: National Bureau of Standardsslope � 1: Stanford University slope � 3: Smithsonian Institution

3. 4.

The experiment involved a substance In the experiment, the substance wascalled . cooled to .

slope � 2: carbon 14 slope � �43�: �273�C

slope � 1: cobalt 60 slope � �34�: �100°C

??

??


x �2 1 4 7

y �3 1 5 9

x 0 2 4 6

y 2 4 6 8

x �2 �1 0 1

y 3 3 3 3

x 0 1 2 3

y 1 4 7 10

Study Guide and InterventionSolving Proportions


Determine whether the pair of ratios �2204� and �

1128� forms a proportion.

Find the cross products.

Since the cross products are not equal, the ratios do not form a proportion.

Solve �1320� � �7

k0�.

�1320�

� �7k0�

Write the equation.

12 � 70 � 30 � k Find the cross products.

840 � 30k Multiply.

�83400

� � �3300k

� Divide each side by 30.

28 � k Simplify. The solution is 28.

Determine whether each pair of ratios forms a proportion.

1. �1170�

, �152� 2. �

69�, �

1128�

3. �182�

, �1105�

4. �175�

, �1332�

5. �79�, �

4693�

6. �284�

, �1228�

7. �47�, �

1721�

8. �2305�

, �3405�

9. �1284�

, �34�

Solve each proportion.

10. �5x

� � �1255�

11. �34� � �

1c2� 12. �

69� � �

1r0�

13. �1264�

� �1z5�

14. �58� � �1

s2�

15. �1t4� � �

1101�

16. �w6� � �

27.8� 17. �

5y� � �16

7.8� 18. �1

x8�

� �376�

2024

1218

�→ 24 · 12 � 288→ 20 · 18 � 360

NAME ________________________________________ DATE ______________ PERIOD _____

A proportion is an equation that states that two ratios are equivalent. To determine whether a pair ofratios forms a proportion, use cross products. You can also use cross products to solve proportions.

Practice: SkillsSolving Proportions

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Determine whether each pair of ratios forms a proportion.

1. �58�, �

23� 2. �

73�, �

164� 3. �

68�, �1

92�

4. �196�, �

161� 5. �

5150�

, �122� 6. �

68�, �

1250�

7. �59�, �

1257�

8. �138�

, �1616�

9. �171�

, �1253�

10. �193�

, �1137�

11. �432�

, �750�

12. �67�, �

3469�

Solve each proportion.

13. �142�

� �9y

� 14. �168�

� �4c� 15. �

7z� � �

8142�

16. �150�

� �w8

� 17. �9x

� � �145�

18. �260�

� �5y

�

19. �59� � �

6r� 20. �n

8� � �

170� 21. �

d5� � �

1820�

22. �5y

� � �1130�

23. �228�

� �3p5�

24. �1t1� � �

11010

�

25. �1m.2� � �

35� 26. �

01..95�

� �1a0�

27. �37� � �4

k.2�

28. �6x.3� � �

158� 29. �

39.6� � �0

b.5�

30. �11.45�

� �4y.2�

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word ProblemsSolving Proportions


NAME ________________________________________ DATE ______________ PERIOD _____

1. USAGE A 12-ounce bottle of shampoolasts Enrique 16 weeks. How longwould you expect an 18-ounce bottleof the same brand to last him?

2. COMPUTERS About 13 out of 20 homeshave a personal computer. On a streetwith 60 homes, how many would youexpect to have a personal computer?

3. SNACKS A 6-ounce package of fruitsnacks contains 45 pieces. How manypieces would you expect in a 10-ouncepackage?

4. TYPING Ingrid types 3 pages in thesame amount of time that Tanya types4.5 pages. If Ingrid and Tanya starttyping at the same time, how manypages will Tanya have typed whenIngrid has typed 11 pages?

5. SCHOOL A grading machine can grade48 multiple-choice tests in 1 minute.How long will it take the machine tograde 300 tests?

6. AMUSEMENT PARKS The waiting time toride a roller coaster is 20 minutes when150 people are in line. How long is thewaiting time when 240 people are inline?

7. PRODUCTION A shop produces 39wetsuits every 2 weeks. How long willit take the shop to produce 429wetsuits?

8. FISH Of the 50 fish that Jim caughtfrom the lake, 14 were trout. Theestimated population of the lake is7,500 fish. About how many troutwould you expect to be in the lake?

Reading to Learn MathematicsSolving Proportions

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1. Write a ratio that compares the number of Calories from fat to the totalnumber of Calories. Write the ratio as a fraction in simplest form.

2. Suppose you plan to eat two such granola bars. Write a ratio comparingthe number of Calories from fat to the total number of Calories.

3. Is the ratio of Calories the same for two granola bars as it is for onegranola bar? Why or why not?

Reading the Lesson4. Complete the sentence: If two ratios form a proportion, then the ratios

are said to be __________.

5. Do the ratios �ab� and �d

c� always form a proportion? Why or why not?

6. Explain how you can use cross products to solve proportions in which oneof the terms is not known.

Helping You Remember7. For the proportion �

ab� and �d

c�, why do you think the products ad and bc are

called cross products?


NAME ________________________________________ DATE ______________ PERIOD _____


People of the United StatesA national census is taken every ten years. The 1990 census revealed thatthere were about 250,000,000 people in the United States, and that about 8 out of 100 of these people were 5–13 years old. To find the number ofpeople in the United States that were 5–13 years old, use the ratio ofpeople 5–13 years old and create a proportion.

�1800�

� �250,0n00,000�

To solve the proportion, find cross products.

8 � 250,000,000 � 2,000,000,000 and n � 100 � 100n

Then divide: 2,000,000,000 100 � 20,000,000.

In 1990, about 20,000,000 people in the United States were 5–13 years old.

Use the approximate ratios in each exercise to create a proportion,given that there were about 250,000,000 people in the United States.Then solve and choose the correct answer from the choices at the right.

1. The United States is a diverse collection of different ________ A. 200,000,000races and ethnic origins. Asians or Pacific Islandersaccounted for about �1

300�

of the population of theUnited States. About how many people of Asian orPacific-Island origin lived in the United States?

2. African-Americans accounted for about �235�

of the ________ B. 22,500,000population of the United States. About how manyAfrican-American people lived in the United States?

3. People of Hispanic origin accounted for about �1900�

________ C. 7,500,000of the population of the United States. About howmany people of Hispanic origin lived in theUnited States?

4. Caucasian people accounted for about �45� of the ________ D. 2,000,000

population of the United States. About how manypeople of white or Caucasian origin lived in theUnited States?

5. People of American-Indian, Eskimo, or Aluet origin ______ E. 30,000,000

accounted for about �1,0800� of the population of the

United States. About how many people of

American-Indian, Eskimo, or Aluet origin lived in

the United States?

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment

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Study Guide and InterventionSimilar Polygons


Determine whether �ABC is similar to �DEF. Explain your reasoning.

�A � �D, �B � �E, �C � �F,

�DAB

E��

46� or �

23�, �

BE

CF�

� �69� or �

23�, �D

ACF�

� �182�

or �23�

The corresponding angles are congruent, and the corresponding sides are proportional.

Thus, �ABC is similar to �DEF.

Given that polygon KLMN � polygon PQRS, write a proportion tofind the measure of P�Q�. Then solve.

The ratio of corresponding sides from polygon KLMN topolygon PQRS is �

43�. Write a proportion with this scale

factor. Let x represent the measure of P�Q�.

�PK

QL� � �

43� K�L� corresponds to P�Q�. The scale factor is �

43

�.

�5x� � �

43� KL � 5 and PQ � x

5 � 3 � x � 4 Find the cross products.

�145� � �

44x� Multiply. Then divide each side by 4.

3.75 � x Simplify.

1. Determine whether the polygons 2. The triangles below are similar. Write abelow are similar. Explain your proportion to find each missing measure.reasoning. Then solve.

12

6 4

815x11

5

124

Kx

3

5

N

LP Q

S RM

4

B

8

E

CA D F

646

12

9

NAME ________________________________________ DATE ______________ PERIOD _____

Two polygons are similar if their corresponding angles are congruent and their corresponding sidesare proportional.


Determine whether each pair of polygons is similar. Explain yourreasoning.

1. 2.

3. 4.

5. 6.

7. 8.

x

6

9.6

14

22.4

9.6

6

10

6 6.5

1.5

3.63.9

x

x

1.8

2.6

6.5

8 8

2.6

44

x

6 7

7

3

3.53.520

8

14

10

74

151

101

150

100

15

8

10

12

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: SkillsSimilar Polygons

Practice: Word ProblemsSimilar Polygons

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NAME ________________________________________ DATE ______________ PERIOD _____

1. JOURNALISM The editor of the schoolnewspaper must reduce the size of agraph to fit in one column. The originalgraph is 2 inches by 2 inches, and thescale factor from the original to thereduced graph is 8:3. Find thedimensions of the graph as it willappear in one column of the newspaper.

2. PHOTOCOPIES Lydia plans to use aphotocopy machine to increase the sizeof a small chart that she has made aspart of her science project. The originalchart is 4 inches by 5 inches. If sheuses a scale factor of 5:11, will thechart fit on a sheet of paper 8�

12� inches

by 11 inches? Explain.

No; it will be 8�45

� in. by 11 in.

3. MICROCHIPS The image of a microchipin a projection microscope measures 8inches by 10 inches. The width of theactual chip is 4 millimeters. How longis the chip?

4. PROJECTIONS A drawing on atransparency is 11.25 centimeters wideby 23.5 centimeters tall. The width ofthe image of drawing projected onto ascreen is 2.7 meters. How tall is thedrawing on the screen?

5. GEOMETRY Polygon ABCD is similar topolygon FGHI. Each side of polygonABCD is 3�

14� times longer than the

corresponding side of polygon FGHI.Find the perimeter of polygon FGHI.

6. KITES A toy company produces twokites whose shapes are geometricallysimilar. Find the length of the missingside of the smaller kite.

25 in.25 in.

30 in.22.5 in.

30 in.xB

A

D

I

H

F

G

C

3 in.

2 in.

5 in.

3 in.

Pre-Activity Complete the Mini Lab at the top of page 178 in your textbook.Write your answers below.

1. Compare the angles of the triangles by matching them up. Identify theangle pairs that have equal measure.

2. Express the ratios �DLK

F�, �

EJK

F�, and �

DL

EJ�

to the nearest tenth.

3. What do you notice about the ratios of the matching sides of matchingtriangles?

Reading the Lesson4. Complete the sentence: If two polygons are similar, then their

corresponding angles are __________, and their corresponding sides are__________.

5. If two polygons have corresponding angles that are congruent, does thatmean that the polygons are similar? Why or why not?

6. If the sides of one square are 3 centimeters and the sides of anothersquare are 9 centimeters, what is the ratio of corresponding sides from the first square to the second square?

Helping You Remember7. Look up the everyday definition of the word similar in a dictionary. How

does the definition relate to what you learned in this lesson?

Reading to Learn MathematicsSimilar Polygons


NAME ________________________________________ DATE ______________ PERIOD _____

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Similar and Congruent FiguresIf a 4-inch by 5-inch photograph is enlarged to an 8-inch by 10-inchphotograph, the photographs are said to be similar. They have the sameshape, but they do not have the same size. If a 4-inch by 5-inch photographis duplicated and a new 4-inch by 5-inch photograph is made, thephotographs are said to be congruent. They have the same size and shape.

In each exercise, identify which of the triangles are congruent toeach other and identify which of the shapes are similar to each other.Use the symbol for � congruence and the symbol � for similarity.

1. 2.

3. 4.

5.


a

b

cd

f

a

bc

d

AB

C

DJ L

H NK M

A B C D

H K LM N

P

Q

R T

AB

T

C

D

Q

G

HJ

LKM

NP

Study Guide and InterventionScale Drawings and Models


INTERIOR DESIGN A designer has made ascale drawing of a living room for oneof her clients. The scale of the drawingis 1 inch � 1�

13� feet. On the drawing, the

sofa is 6 inches long. Find the actuallength of the sofa.

Let x represent the actual length of the sofa. Write and solve a proportion.

The actual length of the sofa is 8 feet.

Find the scale factor for the drawing in Example 1.

Write the ratio of 1 inch to 1�13� feet in simplest form.

� �116

iinn.�.�� Convert 1�

13

� feet to inches.

The scale factor is �116�

or 1:16. This means that each distance on the drawing is �116�

theactual distance.

LANDSCAPING Yutaka has made a scale drawingof his yard. The scale of the drawing is1 centimeter = 0.5 meter.

1. The length of the patio is 4.5 centimeters in thedrawing. Find the actual length.

2. The actual distance between the water faucet andthe pear tree is 11.2 meters. Find the correspondingdistance on the drawing.

3. Find the scale factor for the drawing.

1 in.�1�

13� ft

To find the scale factor for scale drawings and models, write the ratio given by the scale in simplestform.

1 in. 6 in.

1 ft13

x ft�

1 · x � 1 · 613

x � 8

drawing distance → actual distance →

← drawing length← actual length

Find the cross products.

Simplify.

↓ ↓Drawing Scale Actual Length

NAME ________________________________________ DATE ______________ PERIOD _____

1 in. = 1 ft

Sofa

13

1 cm = 0.5 m

Patio

PondPath

Water Faucet

PearTree

Garden

Distances on a scale drawing or model are proportional to real-life distances. The scale is determinedby the ratio of a given length on a drawing or model to its corresponding actual length.

Practice: SkillsScale Drawings and Models

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ARCHITECTURE The scale on a set of architectural drawings for a houseis 1.5 inches � 2 feet. Find the length of each part of the house.

7. What is the scale factor of these drawings?

TOWN PLANNING For Exercises 8–11, use the following information.

As part of a downtown renewal project, businesses have constructeda scale model of the town square to present to the city commissionfor its approval. The scale of the model is 1 inch � 7 feet.

8. The courthouse is the tallest building in the town square. If it is

5�12� inches tall in the model, how tall is the actual building?

9. The business owners would like to install new lampposts that areeach 12 feet tall. How tall are the lampposts in the model?

10. In the model, the lampposts are 3�37� inches apart. How far apart

will they be when they are installed?

11. What is the scale factor?

12. MAPS On a map, two cities are 6�12� inches apart. The actual distance

between the cities is 104 miles. What is the scale of the map?

NAME ________________________________________ DATE ______________ PERIOD _____

Room Drawing Length Actual Length

1. Living Room 15 inches

2. Dining Room 10.5 inches

3. Kitchen 12�34� inches

4. Laundry Room 8�14� inches

5. Hall 13�78� inches

6. Garage 16.5 inches

Practice: Word ProblemsScale Drawings and Models


CAMPUS PLANNING For Exercises 1–3, use thefollowing information.

The local school district has made a scale modelof the campus of Engels Middle School includinga proposed new building. The scale of the modelis 1 inch � 3 feet.

NAME ________________________________________ DATE ______________ PERIOD _____

1. An existing gymnasium is 8 inches tallin the model. How tall is the actualgymnasium?

2. The new building is 22.5 inches fromthe gymnasium in the model. Whatwill be the actual distance from thegymnasium to the new building if itis built?

3. What is the scale factor of the model? 4. MAPS On a map, two cities are 5�34�

inches apart. The scale of the map is�12� inch � 3 miles. What is the actualdistance between the towns?

34�12

� mi

5. TRUCKS The bed of Jerry’s pickup truckis 6 feet long. On a scale model of thetruck, the bed is 8 inches long. What isthe scale of the model?

6 ft

6. HOUSING Marta is making a scaledrawing of her apartment for a schoolproject. The apartment is 28 feet wide.On her drawing, the apartment is 7 inches wide. What is the scale ofMarta’s drawing?

28 ft

Gym

nasi

um

Park

ing

AcademicBuilding

View of Campus from Above

NewBuilding


1. How many units wide is the room?

2. The actual width of the room is 18 feet. Write a ratio comparing thedrawing width to the actual width.

3. Simplify the ratio you found and compare it to the scale shown at thebottom of the drawing.

Reading the Lesson4. Give another example of a scale drawing or scale model that is different

from the examples of scale drawings and scale models given on pages184–185 in your textbook.

5. Complete the sentence: distances on a scale model are __________ todistances in real life.

6. What is the scale factor for a model if part of the model that is 4 inchescorresponds to a real-life object that is 16 inches?

Helping You Remember7. Make a scale drawing of a room, such as your classroom or your bedroom.

Select an appropriate scale so that your drawing is a reasonable size. Besure to indicate your scale on your drawing. Use another piece of paper ifnecessary.

Reading to Learn MathematicsScale Drawings and Models

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NAME ________________________________________ DATE ______________ PERIOD _____


Scale DrawingsThe figure at the right has an area of 6 square units. If the figurerepresented a map, and was drawn to a scale of 1 unit � 3 feet, thelengths of the sides would be 6 ft and 9 ft. So, the figure wouldrepresent an area of 54 square feet.

The ratio of the actual area of the figure to the scale area of thefigure can be expressed as a ratio.

�ascctaulaelaarreeaa

� � �564�

� �19� or 1 to 9

Find the actual area and the scale area of these figures. Thendetermine the ratio of actual area to scale area.

1. Scale: 1 unit � 4 ft 2. Scale: 1 unit � 50 cm

actual area actual area

scale area scale area

ratio ratio

3. Scale: 1 unit � 8 mi 4. Scale: 1 unit � 12 m



ratio ratio

5. Scale: 1 unit � 18 in. 6. Scale: 1 unit � 6 km



ratio ratio

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment

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LIGHTING George is standing next to alightpole in the middle of the day. George’s shadow is 1.5 feet long, and the lightpole’s shadow is 4.5 feet long. If George is 6 feet tall, how tall is the lightpole?

Write a proportion and solve.

George’s shadow → 1.5 6 George’s height

lightpole’s shadow → 4.5 h lightpole’s height

1.5 � h � 4.5 � 6 Find the cross products.

1.5h � 27 Multiply.

�11.5.5h

� � �12.75�

Divide each side by 1.5.

h � 18 Simplify.

The lightpole is 18 feet tall.

1. MONUMENTS A statue casts a shadow 30 feet long. At the same time, a person who is 5 feet tall casts a shadow that is 6 feet long. How tall is the statue?

2. BUILDINGS A building casts a shadow 72 meters long. At the same time, a perking meter that is 1.2 meters tall casts a shadow that is 0.8 meter long. How tall is the building?

3. SURVEYING The two triangles shown in the figure are similar. Find the distance d across Red River. 1 m

.9 m

1.8 m

Red River

d

h ft

72 m

1.2 m

0.8 m

h ft

30 ft

5 ft

6 ft

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionIndirect Measurement

Distances or lengths that are difficult to measure directly can sometimes be found using the propertiesof similar polygons and proportions. This kind of measurement is called indirect measurement.

h ft

6 ft

4 ft12 1 ft1

2

→→

�

Practice: SkillsIndirect Measurement


Write a proportion and solve the problem.

1. HEIGHT How tall is Becky? 2. FLAGS How tall is the flagpole?

3. BEACH How deep is the water 4. ACCESSIBILITY How high is the ramp50 feet from shore? when it is 2 feet from the building?

(Hint: �ABE � �ACD)

5. AMUSEMENT PARKS The triangles in 6. CLASS CHANGES The triangles in the figurethe figure are similar. How far is the are similar. How far is the entrance towater ride from the roller coaster? the gymnasium from the band room?Round to the nearest tenth.

45 m

Information Booth

Water Ride

Ferris Wheel

Roller Coaster

Park Entrance21 m10 m

d m

30 m

25 m

Tennis Court

Band Room

Gymnasium

Cafeteria

Fountain

32 m

d m

2 ft

h ftA

BC

DE20 ft

2.5 fth ft

50 ft8 ft

1 ft

9 ft

h ft

6 ft12

31 ft12

7 ft

3 fth ft

4 ft

NAME ________________________________________ DATE ______________ PERIOD _____


NAME ________________________________________ DATE ______________ PERIOD _____

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Practice: Word ProblemsIndirect Measurement

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1. HEIGHT Paco is 6 feet tall and casts a12-foot shadow. At the same time,Diane casts an 11-foot shadow. How tallis Diane?

2. LIGHTING If a 25-foot-tall house casts a75-foot shadow at the same time that astreetlight casts a 60-foot shadow, howtall is the streetlight?

3. FLAGPOLE Lena is 5�12� feet tall and casts

an 8-foot shadow. At the same time, aflagpole casts a 48-foot shadow. Howtall is the flagpole?

4. LANDMARKS A woman who is 5 feet5 inches tall is standing near the Space Needle in Seattle, Washington;she casts a 13-inch shadow at the sametime that the Space Needle casts a121-foot shadow. How tall is the SpaceNeedle?

5. NATIONAL MONUMENTS A 42-footflagpole near the WashingtonMonument casts a shadow that is14 feet long. At the same time, theWashington Monument casts a shadowthat is 185 feet long. How tall is theWashington Monument?

6. ACCESSIBILITY A ramp slopes upwardfrom the sidewalk to the entrance of abuilding at a constant incline. If theramp is 2 feet high when it is 5 feetfrom the sidewalk, how high is theramp when it is 7 feet from thesidewalk?

5 ft

2 ft


NAME ________________________________________ DATE ______________ PERIOD _____


1. How is the caveman measuring the distance to the Sun?

Reading the Lesson2. Complete the following sentence.

When you solve a problem using shadow reckoning, the objects beingcompared and their shadows form two sides of _______________.

3. Suppose that you are standing near a building and you see the shadowscast by you and the building. If you know the length of each of theseshadows and you know how tall you are, write a proportion in words thatyou can use to find the height of the building.

4. STATUE If a statue casts a 6-foot shadow and a 5-foot mailbox casts a4-foot shadow, how tall is the statue?

Helping You Remember5. Work with a partner. Have your partner draw two triangles that are

similar with the lengths of two corresponding sides labeled and thelength of one additional side labeled. Tell your partner how to write aproportion to solve for the length of the side corresponding to theadditional side labeled.

Reading to Learn MathematicsIndirect Measurement


Indirect MeasurementA proportion can be used to determine the heightof tall structures if three variables of the proportionare known. The three known variables are usuallythe height a of the observer, the length b of theobserver’s shadow, and the length d of thestructure’s shadow. However, a proportion can besolved given any three of the four variables.

This chart contains information about various observers and tallbuildings. Use proportions and your calculator to complete the chartof tall buildings of the world.


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a

b

c

d

ab

cd

�

Height ofObserver

Length ofShadow

BuildingLocation

Height ofBuilding

Length ofShadow

1. 5 ft 8 in. Natwest,London 80 ft

2. 4 ft 9 in. Columbia SeafirstCenter, Seattle 954 ft 318 ft

3. 5 ft 10 in. 14 in. Wachovia Building,Winston-Salem 410 ft

4. 15 in. Waterfront Towers,Honolulu 400 ft 83 ft 4 in.

5. 6 ft CN Tower,Toronto 1,821 ft 303 ft 6 in.

6. 5 ft 9 in. 1 ft 11 in. Gateway Arch,St. Louis 630 ft

7. 5 ft 3 in. 1 ft 9 in. Eiffel Tower,Paris 328 ft

8. 8 in. Texas CommerceTower, Houston 1,002 ft 167 ft

9. 5 ft 6 in. 11 in. John HancockTower, Boston 131 ft 8 in.

10. 5 ft 4 in. 8 in. Sears Tower,Chicago 181 ft 9 in.

11. 5 ft 6 in. Barnett Tower,Jacksonville 631 ft 105 ft 2 in.


Graph �ABC with vertices A(�2, �1),B(2, 3), and C(2, �1). Then graph its image �A�B�C�after a dilation with ascale factor of �

32�.

A(�2, �1) → ��2 � �32�, �1 � �

32�� → A��3, ��

32��

B(2, 3) → �2 � �32�, 3 � �

32�� → B�3, 4�

12��

C(2, �1) → �2 � �32�, �1 � �

32�� → C�3, ��

32��

Segment M�N� is a dilation of segment MN. Find the scale factor ofthe dilation and classify it as an enlargement or a reduction.

Write the ratio of the x- or y-coordinate of one vertex of thedilated figure to the x- or y-coordinate of the correspondingvertex of the original figure. Use the x-coordinates of N(1, �2)and N(2, �4).

� �21� or 2

The scale factor is 2. Since the image is larger than the originalfigure, the dilation is an enlargement.

1. Polygon ABCD has vertices A(2, 4), B(�1, 5), C(�3, �5), and

D(3, �4). Find the coordinates of its image after a dilation

with a scale factor of �12�. Then graph polygon ABCD and its

dilation.

2. Segment PQ is a dilation of segment PQ. Find the scale

factor of the dilation and classify it as an enlargement or a

reduction.

x-coordinate of point N��x-coordinate of point N

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionDilations

The image produced by enlarging or reducing a figure is called a dilation.

y

xO

y

xO

MM

N

N

y

xO

y

xO

PP

Q Q


Find the coordinates of the vertices of triangle A�B�C� after triangleABC is dilated using the given scale factor. Then graph triangle ABCand its dilation.

1. A(1, 1), B(1, 3), C(3, 1); scale factor 3 2. A(�2, �2), B(�1, 2), C(2, 1); scale factor 2

3. A(�4, 6), B(2, 6), C(0, 8); scale factor �12� 4. A(�3, �2), B(1, 2), C(2, �3); scale factor 1.5

Segment P�Q� is a dilation of segment PQ. Find the scale factor of the dilationand classify it as an enlargement or a reduction.

5. 6.

2;

7. 8.

NAME ________________________________________ DATE ______________ PERIOD _____

Less

on

X–2

Practice: SkillsDilations

Less

on

4–8

y

xO

y

xO

y

xO

y

xO

y

xO

P

Q

P

Q

y

xOP

Q

P

Q

y

xO

P

P

QQ

y

xO

PP

Q

Q


NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word ProblemsDilations

1. EYES Dave’s optometrist used medicineto dilate his eyes. Before dilation, hispupils had a diameter of 4.1millimeters. After dilation, his pupilshad a diameter of 8.2 millimeters.What was the scale factor of thedilation?

2. BIOLOGY A microscope increases thesize of objects by a factor of 8. Howlarge will a 0.006 millimeterparamecium appear?

3. PHOTOGRAPHY A photograph wasenlarged to a width of 15 inches. If thescale factor was �

32�, what was the width

of the original photograph?

4. MOVIES Film with a width of 35millimeters is projected onto a screenwhere the width is 5 meters. What isthe scale factor of this enlargement?

�1,0

700�

5. PHOTOCOPYING A 10-inch long copy ofa 2.5-inch long figure needs to be madewith a copying machine. What is theappropriate scale factor?

6. MODELS A scale model of a boat isgoing to be made using a scale of �5

10�

.If the original length of the boat is 20 meters, what is the length of themodel?

7. MODELS An architectural model is 30 inches tall. If the scale used to buildthe model is �1

120�

, what is the height ofthe actual building?

8. ADVERTISING An advertiser needs a4-inch picture of a 14-foot automobile.What is the scale factor of thereduction?

�412�


NAME ________________________________________ DATE ______________ PERIOD _____

Less

on

X–2

Pre-Activity Complete the Mini Lab at the top of page 194 in your textbook.Write your answers below.

1. Multiply each coordinate by 2 to find the coordinates of points A, B,and C.

2. On the same coordinate plane, graph points A, B, and C. Then draw �ABC.

3. Determine whether �ABC � �ABC. Explain your reasoning.

Reading the Lesson4. If you are given the coordinates of a figure and the scale factor of a

dilation of that figure, how can you find the coordinates of the newfigure?

5. When you graph a figure and its image after a dilation, how can youcheck your work?

Helping You Remember6. Complete the table below to help you remember the effects of different

scale factors.

Reading to Learn MathematicsDilations

Less

on

4–8

If the scale factor is Then the dilation is

between 0 and 1

greater than 1

equal to 1

y

xO


Dilation and AreaA dilation of a shape creates a new shape that is similar to theoriginal. The ratio of the new image to the original is called thescale factor.

Plot and draw each shape. Then perform the dilation ofeach shape using a scale factor of two. After the new imagehas been drawn, determine the area of both the originalshape and its dilation.

1. A(2, 1), B(7, 1), C(4, 4)

Area of original ________

Area of dilation ________

2. circle with radius (1, 2) to (4, 2)

Area of original ________

Area of dilation ________

3. R(�3, 2), E(�3, �2), C(4, �2), I(4, 2) 4. S(�3, 3), Q(�3, �3), A(3, �3), R(3, 3)

Area of original ________ Area of original ________

Area of dilation ________ Area of dilation ________

5. What general statement can be made about the area of a figure whencompared to its area after being dilated by scale factor 2?

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment

y

xO

Write the letter for the correct answer in the blank at the right of each question.

1. Express 4 inches:32 inches in simplest form.A. 8:1 B. 1:8 C. 2:16 D. 16:1 1.

2. Express 18 blue-eyed students to 20 brown-eyed students in simplest form.F. 3 to 4 G. 9 to 10 H. 4 to 5 I. 90 to 100 2.

3. Express 150 tickets for 30 students as a unit rate.

A. 5 tickets per student B. �15� ticket per student

C. 150 tickets per student D. �310�

ticket per student 3.

4. Express 12 miles in 5 hours as a unit rate.

F. �152�

mi/h G. 12 mi/h H. 2.4 mi/h I. 2 mi/h 4.

DANCE For Questions 5 and 6, use the table at the right that shows the number of boys at the school dance at different times.

5. Find the rate of change in the number of boys between 6:00 and 6:15.A. 50 boys/min B. 65 boys/min C. 15 boys/min D. 1 boy/min 5.

6. Find the rate of change in the number of boys between 6:15 and 6:18.F. 1 boy/min G. 2 boys/min H. 3 boys/min I. 6 boys/min 6.

7. Find the slope of the line of the graph at the right.

A. 2 B. �12�

C. �2 D. ��12� 7.

For Questions 8 and 9, the points given in each table lie on a line. Find the slope of the line.

8. F. 1 G. 4

H. �14� I. �4 8.

9. A. �23� B. ��

23�

C. �2 D. 3 9.

10. Which pair of ratios form a proportion?

F. �2115�

, �75� G. �1

90�

, �1101�

H. �56�, �

23� I. �1

47�

, �1270�

10.

11. Solve �29� � �3

b6�

.

A. 8 B. 4 C. 2 D. 7 11.

12. Solve �56� � �

1d1�.

F. 8�13� G. 12 H. 13.2 I. �6

56�

12.

y

xO


Chapter 4 Test, Form 1

Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

x 0 3 6 9

y 5 3 1 �1

x �3 1 5 9

y �2 �1 0 1

Time 6:00 6:15 6:18 6:30 6:50

Number of Boys 50 65 71 90 87

13. Which pair of polygons is similar?A. B.

C. D. 13.

14. The triangles shown are similar.Find the missing measure.F. 18.75 G. 7.5H. 48 I. 12 14.

15. MAPS The scale on a map is 1 centimeter � 50 kilometers. Findthe actual distance for a map distance of 3 centimeters.A. 150 km B. 3 km C. 150 cm D. 3 cm 15.

16. MOVIES In a science fiction movie, the model of one of the aliens was12 inches tall. In the movie, the alien was seen as 6 feet tall. Whatwas the scale used?F. 2 in. � 1 ft G. 1 in. � 2 ft H. 1 in. � 6 ft I. 6 in. � 1 ft 16.

17. FLAGS A flagpole casts a 12-foot shadow. A bush next to it is 4 feet talland casts a 2-foot shadow. How tall is the flagpole?A. 24 ft B. 6 ft C. 12 ft D. 36 ft 17.

18. FORESTRY How tall is the tree?F. 15 ft G. 2.4 ftH. 60 ft I. 4.2 ft 18.

19. Triangle ABC has vertices A(�1, 0), B(�3, 4), and C(2, 3). Find the coordinates of vertex A after the triangle is dilated using a scale factor of 2.A. (�1, 2) B. (�2, 0) C. (0, �1) D. (1, 0) 19.

20. PROJECTIONS An image that is 10 inches wide on a transparency is30 inches wide when projected onto a screen. What is the scale factor?

F. 30 G. �110�

H. �13� I. 3 20.

Bonus Write a proportion to find the B:missing measure. Then solve.

x3 m

9 m

6 m

21 m

x ft 6 ft

25 ft 10 ft

15

30

2415

x

4

6

9 8

12

185 3

10

6

5

4

2 5 5

33

322

168

9 5


NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 4 Test, Form 1 (continued)


1. Express 9 inches:3 yards in simplest form.A. 3:1 B. 1:4 C. 12:1 D. 1:12 1.

2. Express 112 passengers to 8 minivans in simplest form.F. 14 to 1 G. 896 to 1 H. 28 to 1 I. 1 to 14 2.

3. Express $10.78 for 11 dozen eggs as a unit rate.A. $0.22/dozen B. $0.89/dozen C. $1.20/dozen D. $0.98/dozen 3.

4. Express 1,211 gallons of water in 28 hours as a unit rate.

F. 85 gal/h G. �1473�

gal/h H. 43�14� gal/h I. 173 gal/h 4.

FOOTBALL For Questions 5 and 6, use the information and graph given. The graph shows the attendance at school football games for each of the past six weeks.

5. Find the rate of change in attendance between week 3 and week 4.A. �25 fans/week B. 25 fans/weekC. 50 fans/week D. 100 fans/week 5.

6. Find the rate of change in attendance between week 1 and week 6.F. �25 fans/week G. 20 fans/week H. 50 fans/week I. 10 fans/week 6.

7. Find the slope of the line.

A. �23� B. ��

23�

C. �32� D. ��

32� 7.


8. F. 5 G. �5H. 0 I. 4 8.

9. A. ��43� B. ��

34�

C. �34� D. �

43� 9.

10. Solve �3a6�

� �38�.

F. �23� G. 12 H. 13.5 I. 96 10.

y

xO

y

x0

300

1 2 3 4 5 6

350

400

450

Attendance atFootball Games

Num

ber o

f Fan

s

Week


Ass

essm

ent

Chapter 4 Test, Form 2A

Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

x 1 5 9 13

y �6 �3 0 3

x �5 0 5 10

y 4 4 4 4

11. FUEL ECONOMY A car uses 40 gallons of gasoline to travel 980 miles.How many miles will the car travel on 5 gallons of gasoline?A. 4.9 mi B. 250 mi C. 175.5 mi D. 122.5 mi 11.

12. The pair of polygons is similar. Use a proportion to find the missing measure.

F. 12.5 G. 15 H. 20 I. 14.5 12.

13. MAPS The distance between two cities on a map is 4�18� inches. Find

the actual distance if the scale on the map is 2 inches � 40 miles.

A. 165 mi B. 82�12� mi C. 41�

14� mi D. 100 mi 13.

14. PROJECTIONS An image that is 28 mm wide on a transparency is 154 mmwide when projected onto a screen. What is the scale factor?

F. �121� G. 5 H. 6 I. �

125� 14.

15. LIGHTING How tall is the streetlight at the right?A. 18 ft B. 5 ftC. 25 ft D. 13 ft 15.

16. ARCHITECTURE A fence post 8.4 feet tall casts a shadow 12.6 feet long. A nearby building casts a shadow 96 feet long. How tall is the building?F. 81 ft G. 72 ft H. 144 ft I. 64 ft 16.

17. Triangle ABC has vertices A(�4, 4), B(1, 0), and C(�1, �2). Findthe coordinates vertex A after the triangle is dilated using a scalefactor of 3.5.A. (�14, 14) B. (14, �14) C. (14, 14) D. (�14, �14) 17.

18. Segment D�E� with endpoints D�(�4, 8) and E�(2, �2) is a dilationof segment DE with endpoints D(�9, 12) and E(3, �3). Find thescale factor of the dilation.

F. �32� G. �

23� H. �

31� I. �

13� 18.

Bonus The ratio of red marbles in a bag to green marbles is 2:3. B:If two red marbles are taken away, the ratio becomes 1:2.How many red marbles are in the bag?

x ft

10 ft

5 ft

2 ft

x6

10

12

12.5

7.5

NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 4 Test, Form 2A (continued)



1. Express 10 inches:5 feet in simplest form.A. 1:6 B. 2:1 C. 1:2 D. 1:5 1.

2. Express 35 wins to 25 losses in simplest form.F. 5 to 7 G. 13 to 10 H. 6 to 5 I. 7 to 5 2.


3. $11.70 for 13 pounds of grapesA. $0.90/lb B. $9.90/lb C. $0.09/lb D. $9.00/lb 3.

4. 1,350 miles in 24 hours

F. 65 mi/h G. 225 mi/h H. 56�14� mi/h I. �2

425�

mi/h 4.

ENROLLMENT For Questions 5 and 6, use theinformation and graph given. The graphshows the number of girls enrolled at HillElementary for each of the past six years.

5. Find the rate of change in enrollmentbetween year 2 and year 3.A. �10 girls/year B. 30 girls/yearC. 10 girls/year D. 60 girls/year 5.

6. Find the rate of change in enrollmentbetween year 1 and year 6.F. �10 girls/year G. 12 girls/year H. 10 girls/year I. 60 girls/year 6.

7. Find the slope of the line.

A. �12� B. ��

12�

C. 2 D. �2 7.


8. F. �32� G. �

23�

H. ��23� I. ��

32� 8.

9. A. 2 B. �2C. �3 D. 0 9.

10. Solve �58� � �3

c6�

.

F. �425�

G. 22.5 H. 57.6 I. 1�19� 10.

y

xO

y

x0

200

1 2 3 4 5 6

220

240

260

280

Enrollment atHill Elementary

Num

ber o

f Girl

s

Year


Ass

essm

ent

Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 4 Test, Form 2B

x 5 7 9 11

y �3 �3 �3 �3

x �3 �1 1 3

y 7 4 1 �2

11. FUEL ECONOMY A car uses 35 gallons of gasoline to travel 840 miles.How many gallons are used to go 156 miles?A. 19.5 gal B. 7.2 gal C. 188 gal D. 6.5 gal 11.

12. The pair of polygons is similar. Use a proportion to find the missing measure.

F. 6 G. 12 H. 6.75 I. 8.4 12.

13. MAPS The distance between two cities on a map is 2.75 centimeters.Find the actual distance if the scale on the map is1 centimeter � 60 kilometers.A. 165 km B. 21 km C. 180 km D. 150 km 13.

14. PROJECTIONS An image that is 12�12� inches wide on the transparency

is 35 inches wide on a screen. What is the scale factor?

F. �3152�

G. �154� H. 3 I. �

3153�

14.

15.FLAGS How tall is the flagpole?A. 18 ft B. 63 ftC. 21 ft D. 36 ft 15.

16. ARCHITECTURE A 16-foot tree casts a shadow 18 feetlong at the same time that a building casts a 72-footshadow. How tall is the building?F. 81 ft G. 72 ft H. 64 ft I. 96 ft 16.

17. Triangle ABC has vertices A(�2, �4), B(�3, 1), and C(2, 2).Find the coordinates of vertex A after the triangle is dilatedusing a scale factor of 0.5.A. A�(�4, �8) B. A�(�1.5, �3.5) C. A�(�1, �2) D. A�(�4, �2) 17.

18. Segment R�S� with endpoints R�(13.5, 0) and S�(0, 4.5) is adilation of segment RS with endpoints R(�9, 0) and S(0, 3).Find the scale factor of the dilation.

F. �32� G. �

23� H. �

91� I. �

16� 18.

Bonus The ratio of red beans in a bag to green beans is 1:2. B:If two red beans are eaten, the ratio becomes 1:3. Howmany green beans are in the bag?

16 ft

9 ft

4 ft

12

915 x

9

11.25


NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 4 Test, Form 2B (continued)

1. Find the slope of the line. 1.

For Questions 2 and 3, express each ratio in simplest form.

2. 95 girls to 105 boys 2.

3. 84 out of 144 students 3.

4. Express the rate 296 miles in 5 hours as a unit rate. 4.

5. Which is the better buy, 12 reams of paper for $24.50 or5 reams of paper for $15.25? Explain your reasoning. 5.

RAINFALL For Questions 6 and 7, use the information in the table. The table shows the amount of rain in Shawn’s rain gauge at selected times during a recent storm.

6. Find the rate of change in rainfall between 2:10 and 2:15. 6.

7. Find the rate of change in rainfall between 2:30 and 3:00. 7.

8. The points in the table lie on 8.a line. Find the slope of the line. Then graph the line.

9. Find the slope of the line and interpret its meaning as a rate of change. 9.

For Questions 10 and 11, solve each proportion.

10. �4b8�

� �196�

10.

11. �1f2� � �

4505�

11.

y

xO


Chapter 4 Test, Form 2C

Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

y

xO

y

x0

4

1 2 3 4 5 6 7 8 9

812162024283236

Baby-sitting Money

Amou

nt E

arne

d

Number of Hours

Time 2:10 2:15 2:30 3:00

Inches of Rain 0.5 1 1.5 2.1

x �2 0 2 4

y 4 3 2 1

12. SWIMMING Aretha swims 3 laps every 50 seconds. How 12.many laps will she swim in 120 seconds?

13. Determine whether the pair of polygons is similar. 13.Explain your reasoning.

14. The pair of polygons is 14.similar. Write a proportion to find the missing measure.Then solve.

For Questions 15 and 16, the scale on a map is 1 inch � 575 miles. Find the actual distance for each map distance. 15.

15. 3�14� inches 16. 7�

12� inches 16.

17. PLAYGROUND The triangles formed 17.by the slide and the person are similar. How tall is the slide?

18. ROAD SIGNS A road sign casts 18.a shadow that is 4 feet long.At the same time, a 6-foot man standing next to the sign casts a shadow that is 2.4 feet long. How tall is the sign?

19. Polygon ABCD has vertices A��4�12�, 3�, B(2, 5), C��

12�, �1� 19.

and D(�3, �8). Find the coordinates of its image after a

dilation using a scale factor of �12�.

20. In the figure below �X�Y�Z� is a 20.dilation of �XYZ. Find the scale factor of the dilation, and classify it as an enlargement or a reduction.

Bonus A recipe calls for 2 pounds, 8 ounces of apples B:for 8 servings. How many apples, in poundsand ounces, are needed for 12 servings?

y

xO

X� Y�

YX

Z�

Z


NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 4 Test, Form 2C (continued)

8

611

4

3 5.5

6

55

82 2

3.2x

42 in.

26 in.15 in.

1. Find the slope of the line. 1.

For Questions 2 and 3, expresseach ratio in simplest form.

2. 77 out of 121 dentists 2.

3. 85 men to 110 women 3.

4. Express the rate 315 miles in 6 hours as a unit rate. 4.

5. Which is the better buy, $14.60 for 36 juice boxes or $9.50 5.for 24 juice boxes? Explain.

FOOTBALL For Questions 6 and 7, use the information below and in the table. The table shows the total number of tickets sold at the gate by each time shown.

6. Find the rate of change in ticket sales between 5:15 6.and 5:20.

7. Find the rate of change in ticket sales between 5:35 7.and 6:00.

8. The points in the table lie on 8.a line. Find the slope of the line. Then graph the line.

9. Find the slope of the line and interpret its meaning as a rate of change. 9.

For Questions 10 and 11, solve each proportion.

10. �58� � �3

d6�

10.

11. �1356�

� �5r� 11.

12. HEART RATE If a person’s heart beats 96 times in 12.60 seconds, how many times does it beat in 45 seconds?

y

xO


Chapter 4 Test, Form 2D

Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

y

xO

y

x0

1

10 20 30 40 50 60 70 80 90100

23456789

10

Gallo

ns U

sed

Miles Driven

Gasoline Usage

Time 5:15 5:20 5:35 6:00

Total Tickets Sold 27 47 197 1,072

x �4 �1 2 5

y �1 1 3 5

13. Determine whether the 13.pair of polygons is similar.Explain your reasoning.

14. The pair of polygons is 14.similar. Write a proportionto find the missing measure.Then solve.

For Questions 15 and 16, the scale on a map is 1 inch � 240 miles. Find the actual distance for each map distance.

15. �18� inch 15.

16. 2�34� inches 16.

17. FORESTRY How tall is the tree? 17.

18. MONUMENTS A statue casts 18.a shadow 25 feet long. A boystanding next to the statue is4.5 feet tall and casts ashadow that is 3.6 feet long. How tall is the statue? 19.

19. Polygon MNOP has vertices M(�2, �2), N(�3, 3), O(1, 3),and P(3, �1). Find the coordinates of its image after a dilation using a scale factor of �

13�.

20. The figure �D�E�F� is a dilation 20.of �DEF. Find the scale factor of the dilation and classify it as an enlargement or reduction.

Bonus �GHI has vertices at G(–4, 1), H(3, 2) and I(5, –6). B:�GHI is dilated using a scale factor of �

21�, and the

new triangle is then dilated using a scale factor of �23�.

Find the coordinate of the vertices of the new triangle after the second dilation.


NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 4 Test, Form 2D (continued)

4

21

2

38.25

9

8.25

12

11

11

4

5 x

14 ft2.5 ft

4 ft

y

xO 2 4 6 8 10

2

4

6

8

E�

D�

F�E

DF

1. Express 45 inches:3 feet in simplest form. 1.

2. Which is the better buy, 120 peak-time minutes for $24.95 2.or 180 peak-time minutes for $35.95? Explain your reasoning.

For Questions 3 and 4, use the graph and information below. The graph shows a dolphin’s depth below the ocean’s surface as it swims.

3. Find the rate of change in 3.the dolphin’s depth between 1 and 2 minutes.

4. During which time period was 4.the rate of change in depth 0 feet per minute? How can you tell this from the graph?

5. Five days ago there were 6 cells growing in a sample. 5.Today there are 192 cells. Find the rate of change in the number of cells.


6. 7. 6.

7.

8. The points given in the table lie 8.on a line. Find the slope of the line. Then graph the line.

For Questions 9 and 10, the scale on a map is 1 inch � 330 miles. Find the actual distance.

9. 1�12� inches 9.

10. 4.75 inches 10.

11. Solve �p4� � �

01..66�

. 11.


Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 4 Test, Form 3

y

x0

5

1 2 3 4 5 6

101520

Dolphins

Feet

Bel

owW

ater

's Su

rfac

e

Minutes

y

xO

y

xO

x �3 �2 �1 0

y 5 1 �3 �7y

xO

12. TICKET SALES Eight student tickets cost $160.50. How 12.much will 20 student tickets cost?

For Questions 13 and 14, each pair of polygons is similar.Write a proportion to find each missing measure. Then solve. 13.

13. 14.

14.

15. �EFG ~ �HIJ. Each side 15.of �HIJ is 2�

14� times longer

than the corresponding sides of �EFG. Find the perimeter of �EFG.

16. MONUMENTS The St. Louis arch is 630 feet tall. A model 16.of the arch is 9 feet. What is the scale of the model?

17. GEOGRAPHY How wide is 17.Citrus Lake?

18. ARCHITECTURE The Sears Tower in Chicago, Illinois, is 18.443 meters tall. A smaller building nearby casts a shadow 6.8 meters long. At the same time the Sears Tower casts a shadow 8.6 meters long. How tall is the smaller building to the nearest meter?

19. Polygon ABCD has vertices A��4, �13��, B��2�

12�, 8�, 19.

C�2, 3�14��, and D(0, �1). Find the vertices for a dilation

using a scale factor of 2.

20. In the figure �L�M�N� is a dilation 20.of �LMN. Find the scale factor,and classify the dilation as an enlargement or as a reduction.

Bonus After burning for 5 minutes, a 600-gram candle weighs B:540 grams. Assuming the candle burns at the same rate, how many grams will burn away in 32 minutes?

60 yd

30 yd

75 ydx

16

1618

5

5.6255

20 x


NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 4 Test, Form 3 (continued)

12 m

20 m

14 m

H J

I

E G

F

130 m 110 m

55 m

y

xO 2 4 6 8 10

2

4

6

8

L�M�

N�N

ML

Demonstrate your knowledge by giving a clear, concise solution toeach problem. Be sure to include all relevant drawings and justifyyour answers. You may show your solution in more than one way orinvestigate beyond the requirements of the problem. If necessary,record your answer on another piece of paper.

1. Ratios are used to make concrete. A recommended concrete mix is 1 partcement, 2 parts sand, 4 parts gravel, and water to moisten.

a. Explain what is meant by ratio.

b. Write three ratios that describe the concrete mix. Write each ratio in adifferent form.

c. Explain what is meant by a proportion.

d. Suppose 400 pounds of sand were loaded into a mixer. Tell how muchcement and gravel should be added. Show your work.

2. a. Polygons ABCD and EFGH are similar.Explain what this means.

b. In the above polygons, identify the corresponding sides. How can you use this information to find thelengths of the sides B�C�, E�F�, and G�H�?

c. You can also use indirect measurement to find a missing measurement. Draw a diagram illustratingthe following situation. Then solve the problem.Show your work.An 8-foot barber pole casts a shadow 2 feet long. The barber standing

next to the pole is 5�35� feet tall. How long is his shadow?

d. Explain how using a scale drawing to find a measurement is relatedto using similar polygons and indirect measurement.

e. If a dilated image is smaller than the original, is the scale factorlarger or smaller than 1? Explain.


Chapter 4 Extended Response Assessment

Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

A

B

CDH G

E

F

4

9

9

6

12

Write whether each sentence is true or false. If false, replace the underlined wordto make a true sentence.

1. If the slope of a line is �23�, the ratio corresponding to a rise 1.

of 2 is 3.

2. In a proportion, the two cross products are opposites. 2.

3. A simple closed figure in a plane formed by at least three 3.line segments is called a polygon.

4. A proportion is a special kind of ratio in which two 4.quantities with different types of units are compared.

5. The average amount of snow that fell each hour over a 5.period of several hours is an example of a rate of change.

6. If two polygons are scale factors, their corresponding angles 6.are congruent and their corresponding sides are proportional.

7. Distances on a scale drawing are proportional to distances in 7.real life.

8. A comparison of two numbers by division is called a ratio. 8.

9. In a scale drawing, the indirect measurement is determined 9.by the ratio of a given length on the drawing to its corresponding actual length.

10. Slope is the dilation of the vertical change between two 10.points to the horizontal change between the points.

In your own words, define each term.

11. unit rate

12. corresponding parts

congruent (p. 179)

corresponding parts (p. 178)

cross products (p. 170)

dilation (p. 194)

indirect measurement (p. 188)

polygon (p. 178)

proportion (p. 170)

rate (p. 157)

rate of change (p. 160)

ratio (p. 156)

rise (p. 166)

run (p. 166)

scale (p. 184)

scale drawing (p. 184)

scale factor (p. 179)

scale model (p. 184)

similar (p. 178)

slope (p. 166)

unit rate (p. 157)


NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 4 Vocabulary Test/Review


Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


1. 12 goals in 15 attempts 1.

2. 27 winners chosen out of 90 contestants 2.

3. 44 out of 100 dentists 4. 6 cups for each quart 3.

Express each rate as a unit rate. 4.

5. 253 students for 11 teachers 5.

6. $555 for 6 chairs 6.

7. 165 students for 60 computers 7.

SCIENCE Use the information belowand in the table.

Sara decided to study the growth of a plant for her science project. She recorded the height of her plant in the table.

8. Find the rate of change in the height 8.of the plant from week 1 to week 3.

9. Find the rate of change in the height 9.of the plant from week 9 to week 15.

10. During which of these two time periods did the plant grow 10.faster?

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


1. 2. 1.

Solve each proportion. 2.

3. �85� = �1

a5�

3.

4. �13000�

� �6c� 4.

5. �7t� � �

1238�

5.

Chapter 4 Quiz(Lessons 4-1 and 4-2)


Week Height

6 2

3 2 cm

6 2�12� cm

9 4 cm

15 8 cm

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x �2 0 2 4y 1 4 7 10


NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Ass

essm

ent

1. FLAGS A flagpole casts a shadow 9 feet long at the same 1.time that a 6-foot man casts a shadow of 2.5 feet. How tall is the flagpole?

2. FORESTRY A tree casts a shadow 75 feet long at the 2.same time that an 8-foot sign casts a shadow 10 feet long. How tall is the tree?

For Questions 3 and 4, find the coordinates of the vertices of �X�Y�Z� after �XYZ is dilated using the given scale factor.

3. X(�1, �2), Y(2, 1), Z(4, �1); scale factor 3 3.

4. X(3, �2), Y(0, 0), Z(4, 4); scale factor �12� 4.

5. Segment A�B� with endpoints A��12�, 2� and B��1�

12�, 3� is a 5.

dilation of segment AB. If segment AB has endpoints A(2, 8) and B(6, 12), find the scale factor of the dilation. Then classify the dilation as an enlargement or as a reduction.



NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Each pair of polygons is similar. Write a proportion to find each missing measure. Then solve.

1. 2. 1.

2.

For Questions 3 and 4, the scale on a map is 1 inch � 3.40 miles. Find the actual distance for each map distance.

3. �78� inch 4. 5�

12� inches 4.

5. MULTIPLE-CHOICE TEST ITEM Polygon ABCD is similar to polygon PQRS. Each side of polygon ABCD is 1�

12� times

longer than the corresponding side of polygon PQRS.If the perimeter of polygon ABCD is 15 inches, what is the perimeter of polygon PQRS? A. 22�

12� inches B. 10 inches 5.

C. 37 inches D. 16�12� inches

x

912

16

x

20 12

8


1. Express $42 for 4 days in simplest form.A. 1:4 B. 42:1 C. 2:21 D. 21:2 1.

2. Express 154 miles on 7 gallons as a unit rate.F. 22 mi/gal G. 0.05 mi/galH. 147 mi/gal I. 7 mi/gal 2.

3. Express $2.76 for 12 sandwich rolls as a unit rate.A. $4.35/roll B. $2.76/roll C. $0.23/roll D. $12/roll 3.

4. The points given in the table lie on a line. Find the slope of the line.

F. –1 G. 3 H. ��13� I. �3 4.

5. Solve �1c5�

� �1200�

.A. 30 B. 15 C. 13 D. 7.5 5.

SCHOOL For Exercises 6 and 7, use the following table.

6. Find the rate of change in the number of copies between 6.month 1 and month 3.

7. Find the rate of change in the number of copies between 7.month 6 and month 9 to the nearest whole number.

8. GARDENING If it takes Sheila 1.5 hours to plant 8.28 tomato plants, how long will it take her to plant 98 plants?

9. RACECAR A car on a racetrack drove 96 miles in 9.60 minutes. How many miles did it drive in 10 minutes?

10. Find the slope of the line and 10.interpret its meaning as a rate of change.


NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 4 Mid-Chapter Test(Lessons 4-1 through 4-4)

y

nO

10

10 20 30 40 50 60 70 80 90100

2030405060

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f Jui

ce

Number of Students

x 0 3 6 9

y �4 �5 �6 �7

Month 1 3 6 9

Number of Copies Made 420 619 800 1,215

1. Evaluate �x�

�32

y� if x � 5 and y � �3. (Lesson 1-6) 1.

2. Solve �17 � q � 9. (Lesson 1-8) 2.

3. Find �1396�

� �45�. Write in simplest form. (Lesson 2-3) 3.

4. Find 3�23� � 5�

16�. Write in simplest form. (Lesson 2-6) 4.

5. Evaluate 43 � 22. (Lesson 2-8) 5.

6. Find �729�. (Lesson 3-1) 6.

7. Estimate the solution of x2 � 80 to the nearest integer. 7.(Lesson 3-2)

8. Name all sets of numbers to which �49� belongs. 8.(Lesson 3-3)

9. Find the distance between the points (4, 9) and (�3, �5). 9.Round to the nearest tenth. (Lesson 3-6)

10. Express 220 miles on 11 gallons in simplest form. 10.(Lesson 4-1)

11. Express $15.50 for 5 pounds of cashews as a unit rate. 11.(Lesson 4-1)

12. Find the slope of the line.(Lesson 4-3) 12.

13. Solve �45� � �

1y0�. (Lesson 4-4) 13.

14. The scale on a map is 1 inch � 14.40 miles. Find the actual distance if two towns are 2�

14� inches apart on the map.

(Lesson 4-6)

15. A flagpole casts a shadow 10 feet long at the same time 15.that an 6-foot man casts a shadow that is 4 feet long.How tall is the flagpole? (Lesson 4-7)

16. Segment B�C� is a dilation of segment BC. The endpoints 16.are B(�6, 4), C(2, �8), B�(�9, 6) and C�(3, �12). Find the scale factor of the dilation and classify it as an enlargementor as a reduction. (Lesson 4-8)


NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Chapter 4 Cumulative Review(Chapters 1–4)

y

xO

1. Jill purchased a pair of shoes that cost $59.00. After tax, thetotal cost was $63.43. Which equation could be used to findthe amount of the tax? (Lesson 1-8)A. x � 63.43 � 59 B. 59 � x � 63.43C. x � 59 � 63.43 D. x � 63.43 � 59 1.

2. A board that is 49�12� inches long is cut into pieces that are

4�18� inches long. How many pieces are there? (Lesson 2-4)

F. 9 G. 10 H. 11 I. 12 2.

3. The distance between Lakeland and Iceville is 129 kilometers.If there are 1,000 meters in a kilometer, use scientific notationto write the distance from Lakeland to Iceville in meters.(Lesson 2-9)A. 1.29 � 105 B. 1.29 � 102 3.C. 1.29 � 103 D. 1.29 � 10�3

4. The area of a square is 144 square meters. What is theperimeter? (Lesson 3-1)F. 12 meters G. 24 meters H. 48 meters I. 288 meters 4.

5. Randall walked 80 yards east and then walked 50 yards north.How far is Randall from his starting point to the nearest tenth?(Lesson 3-4)A. 62.5 yd B. 94.3 yd C. 130.0 yd D. 8,900.0 yd 5.

6. Find the distance between (�3, 4) and (7, �7). Round to thenearest tenth. (Lesson 3-6)F. 4.6 units G. 10 units H. 14.9 units I. 11 units 6.

7. Which of the following cannot be written as a ratio? (Lesson 4-1)A. $6 out of $10 earned B. $20 for every $100 donated 7.C. $15 less than the average D. $48 for three baseball caps

price

8. A recipe calls for 12�12� pounds of carrots for 60 servings. How

many pounds of carrots are needed for 1,000 servings? (Lesson 4-4)

F. 2,083�13� G. 208�

13� H. 500�

13� I. 4,800 8.

9. Polygons ABC and XYZ are similar.Find the length of Y�Z�. (Lesson 4-5)A. 3 cm B. 1 cm 9.C. 8 cm D. 2 cm

DCBA

IHGF

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IHGF

DCBA

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Ass

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NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____Standardized Test Practice (Chapter 4)

Part 1: Multiple Choice

Instructions: Fill in the appropriate oval for the best answer.

A B

CX Y

Z

9 cm

3 cm8 cm

6 cm

4 cm

10. Evaluate the expression m(n � p) if 10. 11.m � 1�

35�, n � �

29�, and p � �

13�. (Lesson 2-6)

11. Estimate �77� to the nearest tenth.(Lesson 3-3)

12. Find the slope of the line.(Lesson 4-3) 12.

13. A 6-foot man casts a shadow that 13.is 7.5 feet long. A flagpole near the man casts a shadow that is 45 feet long. How tall is the flagpole?(Lesson 4-7)

14. ELECTIONS The table shows the number of people who had voted by each time in Precinct 109.

a. Find the rate of change in the number of voters between 10 A.M. and 12 P.M. Interpret its meaning.

b. During which time period was the rate of change 0? Explain.

c. During which time period was the rate of change the greatest?

Part 3: Extended Response

Instructions: Write your answers below or to the right of the problems.

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

Part 2: Short Response/Grid In

Instructions: Enter your grid in answers by writing each digit of the answer in acolumn box and then shading in the appropriate circle that corresponds to that entry.Write answers to short answer questions in the space provided.


NAME ________________________________________ DATE ______________ PERIOD _____

Standardized Test Practice (continued)

y

xO

Time 8 A.M. 10 A.M. 12 P.M. 2 P.M. 3 P.M.

Number of Voters 25 67 149 275 275

© Glencoe/McGraw-Hill A1 Mathematics: Applications and Concepts, Course 3

An

swer

s

Standardized Test PracticeStudent Recording Sheet (Use with pages 202–203 of the Student Edition.)

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Part 1:

Solve the problem and write your answer in the blank.

For grid in questions, also enter your answer by writing each number or symbolin a box. Then fill in the corresponding circle for that number of symbol.

7. 8. 9. 10.

8. (grid in)

9. (grid in)

10. (grid in)

11. (grid in) 11. 12. 13.

12. (grid in)

13. (grid in)

14.

15.

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

Select the best answer from the choices given and fill in the corresponding oval.

Multiple Choice

1.

2.

3.

4.

5.

6. IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

Part 2: Short Response/Grid in

Record your answers for Questions 16 and 17 on the back of this paper.

Part 3: Extended Response

General Scoring Guidelines• If a student gives only a correct numerical answer to a problem but does not show how he or she

arrived at the answer, the student will be awarded only 1 credit. All extended response questionsrequire the student to show work.

• A fully correct answer for a multiple-part question requires correct responses for all parts of thequestion. For example, if a question has three parts, the correct response to one or two parts of thequestion that required work to be shown is not considered a fully correct response.

• Students who use trial and error to solve a problem must show their method. Merely showing thatthe answer checks or is correct is not considered a complete response for full credit.

Exercise 16 Rubric

Standardized Test PracticeRubrics (Use to score the Extended Response questions on page 203 of the Student Edition.)

Score Specific Criteria4 The 4 points are correctly graphed and a line is drawn through the points. The slope

of the line is correctly determined to be �92�. The value of the slope is translated to

mean that Susan’s rate of pay is $4.50 per hour. The amount of money Susan willmake for 10 hours of work is correctly determined to be $45.

3 The 4 points are correctly graphed and the line is correctly drawn, but acomputational error in finding one of the values is made.

2 The 4 points are correctly graphed and the line is correctly drawn, but two of theother values are incorrect. ORThe 4 points are not correctly graphed and a different line is drawn, but thenumerical answers are all correct for the graph drawn.

1 The 4 points are correctly graphed and the line is correctly drawn, but none of thevalues are correct. ORThe 4 points are not correctly graphed and a different line is drawn, but one or twoof the numerical answers are correct for the graph drawn.

0 Response is completely incorrect.

Score Specific Criteria4 The coordinates of the vertices of the triangle after the dilation using a scale factor

of �23� are found to be A�(�4, 2), B�(2, 4), and C�(4, �6). The graphs of �ABC and this

dilation are correct. A scale factor greater than 1 is given for an enlargement the�ABC. This scale factor is correctly used to find the coordinates of the vertices of thedilation.

3 The work is mostly correct, but a computational error is made in finding thecoordinates of one of the vertices of a dilated figure. ORThe work is mostly correct, but one of the vertices is incorrectly graphed.

2 The graphs of �ABC and its dilation using a scale factor of �23� are correct, but scale

factor for an enlargement is incorrect or not given. ORThe coordinates of the dilations are correctly given, but the graphs are incorrect ornot shown.

1 The coordinates of one of the dilations are correctly given, but the coordinates of theother dilation are incorrect or not given. The graph is incorrect or not shown. ORThe coordinates of the dilation are incorrect or not given and the graph is incorrector not shown, but a correct scale factor of an enlargement is given.

0 Response is completely incorrect.

Exercise 17 Rubric



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arb

les.

4.W

hat

is

anot

her

way

to

wri

te t

he

rati

o 3

to 5

?S

amp

le a

nsw

er:

3:5

or

�3 5�

5.W

hat

mu

st y

ou d

o be

fore

you

can

sim

plif

y th

e ra

tio

30 m

inu

tes

to

8 h

ours

? W

hat

is

the

sim

plif

ied

rati

o?C

onv

ert

min

ute

s to

ho

urs

or

ho

urs

to

min

ute

s;1:

16.

Hel

pin

g Y

ou

Rem

emb

er6.

Wh

en y

ou g

o to

a b

ank

to e

xch

ange

mon

ey o

f on

e cu

rren

cy f

or a

not

her

,th

e ba

nk

use

s a

con

vers

ion

rat

e to

cal

cula

te t

he

amou

nt

of m

oney

in

th

en

ew c

urr

ency

.Fin

d ou

t w

hat

th

e cu

rren

t co

nve

rsio

n r

ate

is t

o ex

chan

geU

.S.d

olla

rs t

o C

anad

ian

dol

lars

at

a lo

cal

ban

k.T

hen

wri

te t

he

rate

as

ara

tio

of o

ne

curr

ency

com

pare

d to

th

e ot

her

.S

amp

le a

nsw

er:

1 U

.S.d

olla

r to

1.5

6 C

anad

ian

do

llars

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Read

ing

to L

earn

Mat

hem

atic

sR

atio

s an

d R

ates

©G

lenc

oe/M

cGra

w-H

ill18

7M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Prac

tice:

Wor

d Pr

oble

ms

Rat

ios

and

Rat

es

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Lesson 4–1

1.C

OO

KIN

GIn

a b

read

dou

gh r

ecip

e,th

ere

are

3 eg

gs f

or e

very

9 c

ups

of

flou

r.E

xpre

ss t

his

rat

io i

n s

impl

est

form

.1:

3

2.W

ILD

LIFE

Den

a co

un

ted

14 r

obin

s ou

t of

150

bird

s.E

xpre

ss t

his

rat

io i

nsi

mpl

est

form

.7:

75

3.IN

VES

TMEN

TSJo

sh e

arn

ed d

ivid

ends

of

$2.1

6 on

54

shar

es o

f st

ock.

Fin

d th

edi

vide

nds

per

sh

are.

$0.0

4/sh

are

4.TR

AN

SPO

RTA

TIO

NW

hen

Den

ise

bou

ght

gaso

lin

e,sh

e pa

id $

18.4

8 fo

r 11

.2ga

llon

s.F

ind

the

pric

e of

gas

olin

e pe

rga

llon

.$1

.65/

gal

5.W

ATE

R F

LOW

Jaco

b fi

lled

his

60-

gall

onba

thtu

b in

5 m

inu

tes.

How

fas

t w

as t

he

wat

er f

low

ing?

12 g

al/m

in

6.TR

AV

ELO

n h

er v

acat

ion

,Ch

arm

ain

e’s

flig

ht

last

ed 4

.5 h

ours

.Sh

e tr

avel

ed95

4 m

iles

.Fin

d th

e av

erag

e sp

eed

ofth

e pl

ane.

212

mi/h

7.H

OU

SIN

GM

r.A

nd

Mrs

.Rom

ero

bou

ght

a 1,

200

squ

are-

foot

hou

se f

or $

111,

600.

How

mu

ch d

id t

hey

pay

per

squ

are

foot

?$9

3/ft

2

8.SH

OPP

ING

A b

reak

fast

cer

eal

com

es i

ntw

o di

ffer

ent

size

d pa

ckag

es.T

he

8-ou

nce

box

cos

ts $

2.88

,wh

ile

the

12-o

un

ce b

ox c

osts

$3.

60.W

hic

h b

ox i

sth

e be

tter

bu

y? E

xpla

in y

our

reas

onin

g.T

he

12-o

z b

ox a

t $0

.30/

oz;

the

8-o

z b

ox c

ost

s $0

.36

per

oz,

but

the

12-o

z b

ox c

ost

s $0

.30

per

oz.



©G

lenc

oe/M

cGra

w-H

ill19

0M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

INC

OM

ET

he

grap

h s

how

s M

r.J

ack

son

’s

ann

ual

in

com

e b

etw

een

199

4 an

d 2

002.

Fin

d t

he

rate

of

chan

ge i

n M

r.J

ack

son

’s

inco

me

bet

wee

n 1

994

and

199

7.

Use

th

e fo

rmu

la f

or t

he

rate

of

chan

ge.

Let

(x 1

,y1)

�(1

994,

48,5

00)

and

(x2,

y 2)�

(199

7,53

,000

).

�y x2 2

– –y x1 1

��5

3 1,0 90 90 7� �

4 18 9, 95 400�

Writ

e th

e fo

rmul

a fo

r ra

te o

f ch

ange

.

��4,

5 300 �S

impl

ify.

��1,

5 100 �E

xpre

ss t

his

rate

as

a un

it ra

te.

Bet

wee

n 1

994

and

1997

,Mr.

Jack

son

’s i

nco

me

incr

ease

d an

av

erag

e of

$1,

500

per

year

.

SUR

FF

or E

xerc

ises

1–3

,use

th

e gr

aph

th

at

show

s th

e av

erag

e d

aily

wav

e h

eigh

t as

m

easu

red

by

an o

cean

bu

oy o

ver

a n

ine-

day

p

erio

d.

1.F

ind

the

rate

of

chan

ge i

n t

he

aver

age

dail

y w

ave

hei

ght

betw

een

day

1 a

nd

day

3.2

ft/d

ay

2.F

ind

the

rate

of

chan

ge i

n t

he

aver

age

dail

y w

ave

hei

ght

betw

een

day

3 a

nd

day

7.0.

5 ft

/day

3.F

ind

the

rate

of

chan

ge i

n t

he

aver

age

dail

y w

ave

hei

ght

betw

een

day

7 a

nd

day

9.�

1.5

ft/d

ay

y

x

Days

79111315

13

57

9

Day

Wav

e H

eigh

t ( 7, 1

4) ( 9, 1

1)

( 3, 1

2)

( 1, 8

)

0

'94

'96

'98

'00

'02

50,0

00

45,0

00

55,0

00

60,0

00

65,0

00

Annual Income ($)

Year

Mr.

Jack

son'

s In

com

e

y

x

1994

, 48,

500

2002

, 57,

000

1997

, 53,

000

0

To f

ind

the

rate

of

chan

ge b

etw

een

two

data

poi

nts,

div

ide

the

diffe

renc

e of

the

y-c

oord

inat

es b

y th

e

diffe

renc

e of

the

x-c

oord

inat

es.T

he r

ate

of c

hang

e be

twee

n (x

1, y

1) a

nd (

x 2,

y 2)

is � xy 22

��y x1 1

�.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Rat

e o

f C

han

ge

©G

lenc

oe/M

cGra

w-H

ill18

9M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Bar

gai

n H

un

tin

gR

ates

are

use

ful

and

mea

nin

gfu

l w

hen

exp

ress

ed a

s a

un

it r

ate.

For

exa

mpl

e,w

hic

h i

s th

e be

tter

bu

y—on

e or

ange

for

$0.

29 o

r12

ora

nge

s fo

r $3

.00?

To

fin

d th

e u

nit

rat

e fo

r 12

ora

nge

s,di

vide

$3.

00 b

y 12

.Th

ere

sult

is

$0.2

5 pe

r or

ange

.If

a sh

oppe

r n

eeds

to

buy

at l

east

12 o

ran

ges,

then

12

oran

ges

for

$3.0

0 is

th

e be

tter

bu

y.

For

eac

h e

xerc

ise

bel

ow,r

ates

are

giv

en i

n C

olu

mn

A a

nd

C

olu

mn

B.I

n t

he

bla

nk

nex

t to

eac

h e

xerc

ise

nu

mb

er,w

rite

th

e le

tter

of

the

colu

mn

th

at c

onta

ins

the

bet

ter

bu

y.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

BAAAABBBAA

OR

ANG

ES

Enric

hmen

tN

AM

E__

____

____

____

____

____

____

____

____

____

__D

ATE

___

____

____

___

PE

RIO

D

____

_

Lesson 4–1

Col

um

n A

Col

um

n B

1 ap

ple

for

$0.1

93

appl

es f

or $

0.59

20 p

oun

ds o

f pe

t fo

od f

or $

14.9

950

pou

nds

of

pet

food

for

$37

.99

A c

ar t

hat

tra

vels

308

mil

es o

n11

gal

lon

s of

gas

olin

eA

car

th

at t

rave

ls 4

06 m

iles

on

14 g

allo

ns

of g

asol

ine

10 f

lopp

y di

scs

for

$8.9

925

flo

ppy

disc

s fo

r $1

9.75

1-ga

llon

can

of

pain

t fo

r $1

3.99

5-ga

llon

bu

cket

of

pain

t fo

r$6

7.45

84 o

un

ces

of l

iqu

id d

eter

gen

tfo

r $1

0.64

48 o

un

ces

of l

iqu

id d

eter

gen

tfo

r $6

.19

5,00

0 sq

uar

e fe

et o

f la

wn

foo

dfo

r $1

1.99

12,5

00 s

quar

e fe

et o

f la

wn

foo

dfo

r $2

9.99

2 co

mpa

ct d

iscs

for

$26

.50

3 co

mpa

ct d

iscs

for

$40

.00

8 pe

nci

ls f

or $

0.99

12 p

enci

ls f

or $

1.49

1,00

0 sh

eets

of

com

pute

rpa

per

for

$8.9

55,

000

shee

ts o

f co

mpu

ter

pape

rfo

r $4

1.99

Answers (Lessons 4-1 and 4-2)

An

swer

s


©G

lenc

oe/M

cGra

w-H

ill19

2M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

ELEC

TIO

NS

For

Exe

rcis

es 1

–3,u

se t

he

tab

le t

hat

sh

ows

the

tota

l n

um

ber

of p

eop

le w

ho

had

vot

ed i

n D

istr

ict

5 at

var

iou

s ti

mes

on

ele

ctio

n d

ay.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice:

Wor

d Pr

oble

ms

Rat

e o

f C

han

ge

1.F

ind

the

rate

of

chan

ge i

n t

he

nu

mbe

rof

vot

ers

betw

een

8:0

0 A.M

.an

d10

:00

A.M

.Th

en i

nte

rpre

t it

s m

ean

ing.

105

vote

rs/h

r;B

etw

een

8:0

0 A.M

.an

d 1

0:00

A.M

.,an

ave

rag

e o

f 10

5 p

eop

le v

ote

d e

ach

ho

ur.

2.F

ind

the

rate

of

chan

ge i

n t

he

nu

mbe

rof

vot

ers

betw

een

10:

00 A

.M.a

nd

1:00

P.M

.Th

en i

nte

rpre

t it

s m

ean

ing.

149

vote

rs/h

r;B

etw

een

10:

00A.M

.an

d 1

:00

P.M

.,an

ave

rag

e o

f14

9 p

eop

le v

ote

d e

ach

ho

ur.

3.D

uri

ng

wh

ich

of

thes

e tw

o ti

me

peri

ods

did

the

nu

mbe

r of

peo

ple

wh

o h

advo

ted

so f

ar i

ncr

ease

fas

ter?

Exp

lain

you

r re

ason

ing.

Bet

wee

n

10:0

0 A.M

.an

d 1

:00

P.M

.;th

e ra

teo

f ch

ang

e is

gre

ater

fo

r th

is t

ime

per

iod

.

4.M

USI

CA

t th

e en

d of

199

9,C

anda

ce h

ad47

CD

s in

her

mu

sic

coll

ecti

on.A

t th

een

d of

200

2,sh

e h

ad 1

34 C

Ds.

Fin

d th

era

te o

f ch

ange

in

th

e n

um

ber

of C

Ds

inC

anda

ce’s

col

lect

ion

bet

wee

n 1

999

and

2002

.29

CD

s/yr

5.FI

TNES

SIn

199

2,th

e pr

ice

of a

n a

nn

ual

mem

bers

hip

at

Mr.

Jen

sen

’s h

ealt

h c

lub

was

$22

5.In

200

2,th

e pr

ice

of t

he

sam

e m

embe

rsh

ip w

as $

319.

50.F

ind

the

rate

of

chan

ge i

n t

he

pric

e of

th

ean

nu

al m

embe

rsh

ip b

etw

een

199

2 an

d20

02.

$9.4

5/yr

6.H

IKIN

GL

ast

Sat

urd

ay F

um

io a

nd

Kis

hi

wen

t h

ikin

g in

th

e m

oun

tain

s.W

hen

they

sta

rted

bac

k at

2:0

0 P.

M.,

thei

rel

evat

ion

was

3,5

60 f

eet

abov

e se

ale

vel.

At

6:00

P.M

.,th

eir

elev

atio

n w

as2,

390

feet

.Fin

d th

e ra

te o

f ch

ange

of

thei

r el

evat

ion

bet

wee

n 2

:00

P.M

.an

d6:

00 P

.M.

Th

en i

nte

rpre

t it

s m

ean

ing.

�29

2.5

ft/h

;Th

ey d

esce

nd

ed a

tan

ave

rag

e ra

te o

f 29

2.5

ft/h

.

Tim

e8:

00 A

.M.

10:0

0 A.M

.1:

00 P

.M.

4:30

P.M

.7:

00 P

.M.

Nu

mb

er o

f V

oter

s14

135

179

81,

008

1,75

3

©G

lenc

oe/M

cGra

w-H

ill19

1M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

TEM

PER

ATU

RE

Use

th

e ta

ble

bel

ow t

hat

sh

ows

the

hig

h t

emp

erat

ure

of

a ci

ty f

or t

he

firs

t p

art

of A

ugu

st.

1.F

ind

the

rate

of

chan

ge i

n t

he

hig

h t

empe

ratu

re b

etw

een

Au

gust

1 a

nd

Au

gust

5.

2°/d

ay

2.F

ind

the

rate

of

chan

ge i

n t

he

hig

h t

empe

ratu

re b

etw

een

Au

gust

5 a

nd

Au

gust

14.

1°/d

ay

3.D

uri

ng

wh

ich

of

thes

e tw

o ti

me

peri

ods

did

the

hig

h t

empe

ratu

re r

ise

fast

er?

bet

wee

n A

ug

ust

1 a

nd

Au

gu

st 5

4.F

ind

the

rate

of

chan

ge i

n t

he

hig

h t

empe

ratu

re b

etw

een

Au

gust

14

and

Au

gust

15.

Th

en i

nte

rpre

t it

s m

ean

ing.

0°/d

ay;

Bet

wee

n A

ug

ust

14

and

Au

gu

st 1

5,th

e h

igh

tem

per

atu

re d

id n

ot

chan

ge.

CO

MPA

NY

GR

OW

THU

se t

he

grap

h t

hat

sh

ows

the

nu

mb

er o

f em

plo

yees

at

a c

omp

any

bet

wee

n 1

994

and

200

2.

5.F

ind

the

rate

of

chan

ge i

n t

he

nu

mbe

r of

em

ploy

ees

betw

een

199

4 an

d 19

96.

7 em

plo

yees

/yr

6.F

ind

the

rate

of

chan

ge i

n t

he

nu

mbe

r of

em

ploy

ees

betw

een

199

6 an

d 19

99.

3 em

plo

yees

/yr

7.D

uri

ng

wh

ich

of

thes

e tw

o ti

me

peri

ods

did

the

nu

mbe

r of

em

ploy

ees

grow

fas

ter?

bet

wee

n 1

994

and

199

6

8.F

ind

the

rate

of

chan

ge i

n t

he

nu

mbe

r of

em

ploy

ees

betw

een

199

9 an

d 20

02.T

hen

in

terp

ret

its

mea

nin

g.�

1 em

plo

yee/

yr;

Bet

wee

n 1

999

and

200

2,th

e n

um

ber

of

emp

loye

esd

ecre

ased

an

ave

rag

e o

f 1

emp

loye

e/yr

.

y

x

Number of Employees 1020304050 019

9419

9619

9820

0020

02

Year

Com

pany

Gro

wth

( 199

9, 4

1)

( 200

2, 3

8)( 1

996,

32)

( 199

4, 1

8)

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice:

Ski

llsR

ate

of

Ch

ang

e

Lesson 4–2

Dat

e1

514

15

Hig

h T

emp

erat

ure

(ºF

)85

9310

210

2



©G

lenc

oe/M

cGra

w-H

ill19

4M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

An

alyz

ing

Gra

ph

sA

gra

ph c

an b

e u

sed

to r

epre

sen

t m

any

real

-lif

e si

tuat

ion

s.G

raph

s su

ch a

sth

ese

ofte

n h

ave

tim

e as

th

e di

men

sion

on

th

e h

oriz

onta

l ax

is.B

y an

alyz

ing

the

rate

of

chan

ge o

f di

ffer

ent

part

s of

a g

raph

,you

can

dra

w c

oncl

usi

ons

abou

t w

hat

was

hap

pen

ing

in t

he

real

-lif

e si

tuat

ion

at

that

tim

e.

TRA

VEL

Th

e gr

aph

at

the

righ

t re

pre

sen

ts t

he

spee

dof

a c

ar a

s it

tra

vels

alo

ng

the

road

.Des

crib

e w

hat

is h

app

enin

g in

th

e gr

aph

.

•A

t th

e or

igin

,th

e ca

r is

sto

pped

.

•W

her

e th

e li

ne

show

s a

fast

,pos

itiv

e ra

te o

fch

ange

,th

e ca

r is

spe

edin

g u

p.

•T

hen

th

e ca

r is

goi

ng

at a

con

stan

t sp

eed,

show

n b

y th

e h

oriz

onta

l pa

rt o

f th

e gr

aph

.

•T

he

car

is s

low

ing

dow

n w

her

e th

e gr

aph

show

s a

neg

ativ

e ra

te o

f ch

ange

.

•T

he

car

stop

s an

d st

ays

stil

l fo

r a

shor

t ti

me.

Th

en i

t sp

eeds

up

agai

n.

Th

e st

arti

ng

and

stop

pin

g pr

oces

s re

peat

s co

nti

nu

ally

.

An

alyz

e ea

ch g

rap

h.

1.A

shle

y is

rid

ing

her

bic

ycle

alo

ng

a sc

enic

tra

il.

Des

crib

e w

hat

is

hap

pen

ing

in t

he

grap

h.

Sam

ple

an

swer

:A

t th

e b

egin

nin

g,A

shle

y is

sit

tin

g

still

.Sh

e sp

eed

s u

p q

uic

kly,

then

slo

ws

do

wn

a li

ttle

.Th

en s

he

trav

els

at t

he

sam

e sp

eed

fo

r a

sho

rt t

ime.

Ash

ley

spee

ds

up

q

uic

kly

and

tra

vels

at

the

sam

e sp

eed

fo

r a

lon

g t

ime.

Fin

ally

,sh

e sl

ow

s d

ow

n s

low

ly

and

sto

ps.

2.T

he

grap

h s

how

s th

e de

pth

of

wat

er i

n a

pon

d as

you

trav

el o

ut

from

th

e sh

ore.

Des

crib

e w

hat

is

hap

pen

ing

in t

he

grap

h.

Sam

ple

an

swer

:A

t th

e b

egin

nin

g,t

he

wat

er g

ets

dee

per

slo

wly

.T

hen

th

ere

is a

fas

t in

crea

se in

dep

th.T

he

dep

th is

th

e sa

me

for

a sh

ort

dis

tan

ce,t

hen

in

crea

ses

slo

wly

fo

r a

lon

g d

ista

nce

.Th

en

the

dep

th d

ecre

ases

fo

r a

sho

rt d

ista

nce

b

efo

re b

egin

nin

g t

o in

crea

se a

gai

n.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enric

hmen

t

car i

s ac

cele

ratin

gm

aint

aini

ng s

peed

car i

s sl

owin

g do

wn

car i

s st

oppe

d

Speed (mph)

Tim

e (m

in)

0 Speed (ft/s)

Tim

e (m

in)

0 Depth (ft)

Dis

tan

ce f

rom

Sh

ore

(ft

)0

Lesson 4–2

Pre-

Act

ivit

yR

ead

th

e in

tro

du

ctio

n a

t th

e to

p o

f p

age

160

in y

ou

r te

xtb

oo

k.W

rite

yo

ur

answ

ers

bel

ow

.

1.B

y h

ow m

any

bear

s di

d A

lici

a’s

coll

ecti

on i

ncr

ease

bet

wee

n 1

997

and

1999

? B

etw

een

199

9 an

d 20

02?

14;1

5

2.B

etw

een

wh

ich

yea

rs d

id A

lici

a’s

coll

ecti

on i

ncr

ease

th

e fa

stes

t?b

etw

een

199

7 an

d 1

999;

Sam

ple

an

swer

:Wh

ile t

he

incr

ease

bet

wee

n e

ach

tim

e p

erio

d is

nea

rly

the

sam

e,th

e fi

rst

incr

ease

occ

urs

ove

r a

sho

rter

am

ou

nt

of

tim

e.

Rea

din

g t

he

Less

on

3.W

hat

doe

s a

rate

of

chan

ge m

easu

re o

n a

gra

ph?

Sam

ple

an

swer

:h

ow

fas

t a

seg

men

t g

oes

up

or

do

wn

wh

en t

he

gra

ph

is r

ead

fro

m le

ft t

o r

igh

t

4.O

n a

gra

ph,w

hat

doe

s it

mea

n w

hen

a r

ate

of c

han

ge i

s n

egat

ive?

Sam

ple

an

swer

:Th

ere

is a

dec

reas

e in

y-v

alu

es.

5.C

ompl

ete

the

sen

ten

ce:W

hen

a q

uan

tity

doe

s n

ot c

han

ge o

ver

a pe

riod

of

tim

e,it

is

said

to

hav

e a

____

____

__ r

ate

of c

han

ge.

zero

Hel

pin

g Y

ou

Rem

emb

er6.

Wri

te o

ut

in w

ords

th

e fo

rmu

la f

or f

indi

ng

a ra

te o

f ch

ange

bet

wee

n t

wo

data

poi

nts

(x 1

,y1)

an

d (x

2,y 2

).S

amp

le a

nsw

er:T

o f

ind

th

e ra

teo

f ch

ang

e b

etw

een

tw

o d

ata

po

ints

,div

ide

the

dif

fere

nce

inth

e y-

coo

rdin

ates

by

the

dif

fere

nce

in t

he

x-co

ord

inat

es.

Read

ing

to L

earn

Mat

hem

atic

sR

ate

of

Ch

ang

e

©G

lenc

oe/M

cGra

w-H

ill19

3M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___


An

swer

s


Prac

tice:

Ski

llsS

lop

e

©G

lenc

oe/M

cGra

w-H

ill19

6M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Fin

d t

he

slop

e of

eac

h l

ine.

1.�1 3�

2.�3 2�

3.�

�3 2�

4.�

�1 5�5.

06.

�2

Th

e p

oin

ts g

iven

in

eac

h t

able

lie

on

a l

ine.

Fin

d t

he

slop

e of

th

e li

ne.

Th

en g

rap

h t

he

lin

e.

7.8.

9.

�1 3��

�1 2��

1

10.

11.

12.

0�3 2�

��3 4�

y

xO

y

xO

O

y

xO

y

xO

y

xO

y

xO

y

xO

y

xO

y

xO

y

xO

y

xO

y

xON

AM

E__

____

____

____

____

____

____

____

____

____

__D

ATE

___

____

____

___

PE

RIO

D

____

_

x�

4�

20

2

y3

33

3

x�

7�

5�

3�

1

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6�

30

3

x�

8�

40

4

y8

52

�1

x�

2�

10

1

y2

10

�1

x1

35

7

y6

54

3

x0

36

9

y1

23

4

Lesson 4–3

Stud

y Gu

ide

and

Inte

rven

tion

Slo

pe

©G

lenc

oe/M

cGra

w-H

ill19

5M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Fin

d t

he

slop

e of

th

e li

ne

in t

he

grap

h.

Ch

oose

tw

o po

ints

on

th

e li

ne.

Th

e ve

rtic

al c

han

ge f

rom

poi

nt

Ato

poi

nt

Bis

4 u

nit

s w

hil

e th

e h

oriz

onta

l ch

ange

is

2 u

nit

s.

slop

e �

�r ri us ne �D

efin

ition

of

slop

e

��4 2�

The

ris

e is

4,

and

the

run

is 2

.

�2

Sim

plify

.

Th

e sl

ope

of t

he

lin

e is

2.

Th

e p

oin

ts i

n t

he

tab

le l

ie o

n a

lin

e.F

ind

th

e sl

ope

of t

he

lin

e.

slop

e �

�r ri us ne ��c ch ha an ng ge e

i in ny x

�

�� 34 �

or �

�4 3�

Th

e sl

ope

of t

he

lin

e is

��4 3�.

Fin

d t

he

slop

e of

eac

h l

ine.

1.�3 2�

2.�3 5�

3.�

�1 4�

Th

e p

oin

ts g

iven

in

eac

h t

able

lie

on

a l

ine.

Fin

d t

he

slop

e of

th

e li

ne.

4.�3 2�

5.�

�1 5�

y

xO

y

xO

y

xO

The

slo

pe

of a

line

is t

he r

atio

of

the

rise,

or

vert

ical

cha

nge,

to

the

run,

or

horiz

onta

l cha

nge.

y

xOris

e: 4

run:

2

B

A

x�

21

47

y5

1�

3�

7

��

�

�

�

�

� 3

x�

50

510

y4

32

1

x3

57

9

y�

12

58

� 3

� 3

� 4

� 4

� 4

← ←



Pre-

Act

ivit

yR

ead

th

e in

tro

du

ctio

n a

t th

e to

p o

f p

age

166

in y

ou

r te

xtb

oo

k.W

rite

yo

ur

answ

ers

bel

ow

.

1.P

ick

seve

ral

pair

s of

poi

nts

fro

m t

hos

e pl

otte

d an

d fi

nd

the

rate

of

chan

gebe

twee

n t

hem

.Wri

te e

ach

rat

e in

sim

ples

t fo

rm.

All

rate

s o

f ch

ang

e eq

ual

8 f

t/s.

2.W

hat

is

tru

e of

th

ese

rate

s?T

hey

are

all

the

sam

e.

Rea

din

g t

he

Less

on

3.S

lope

can

be

posi

tive

,neg

ativ

e,or

zer

o.F

or e

ach

on

e of

th

ese

poss

ibil

itie

sdr

aw a

n e

xam

ple

of a

lin

e w

ith

th

at k

ind

of s

lope

.

Sam

ple

an

swer

:S

amp

le a

nsw

er:

Sam

ple

an

swer

:p

osi

tive

slo

pe

neg

ativ

e sl

op

eze

ro s

lop

e

Hel

pin

g Y

ou

Rem

emb

er4.

Th

e sl

ope

of a

lin

e is

def

ined

by

the

rise

com

pare

d to

th

e ru

n b

etw

een

an

ytw

o po

ints

on

th

e li

ne.

Th

ink

abou

t th

e w

ords

ris

ean

d ru

n.H

ow c

an y

oure

mem

ber

wh

ich

wor

d re

pres

ents

ver

tica

l ch

ange

an

d w

hic

h w

ord

repr

esen

ts h

oriz

onta

l ch

ange

?S

amp

le a

nsw

er:

Ris

eis

a v

erti

cal

acti

on

,as

in r

isin

gfr

om

yo

ur

seat

at

the

tab

le;

run

is a

ho

rizo

nta

l act

ion

,as

in r

un

nin

gar

ou

nd

a t

rack

.

y

xO

y

xO

y

xORe

adin

g to

Lea

rn M

athe

mat

ics

Slo

pe

©G

lenc

oe/M

cGra

w-H

ill19

8M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Lesson 4–3

Prac

tice:

Wor

d Pr

oble

ms

Slo

pe

©G

lenc

oe/M

cGra

w-H

ill19

7M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

FLO

WER

SF

or E

xerc

ises

1 a

nd

2,u

se

LON

G D

ISTA

NC

EF

or E

xerc

ises

3–6

,use

th

e gr

aph

th

at s

how

s th

e d

epth

of

the

the

grap

h t

hat

com

par

es t

he

cost

s of

w

ater

in

a v

ase

of f

low

ers

over

8 d

ays.

lon

g d

ista

nce

ph

one

call

s w

ith

th

ree

dif

fere

nt

com

pan

ies.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

y

x01

12

34

56

78

910

2345678910

Dep

th o

f Wat

er in

Vas

e

Depth (in.)

Day

1.F

ind

the

slop

e of

th

e li

ne.

��3 4�

2.In

terp

ret

the

mea

nin

g th

is s

lope

as

a

rate

of

chan

ge.

Th

e d

epth

of

the

wat

er is

dec

reas

ing

by

�3 4�in

chea

ch d

ay.

y

x0

12

34

56

78

9

0.50

1.00

1.50

2.00

2.50

Long

Dis

tanc

e Ch

arge

s

Cost ($)

Leng

th o

f Cal

l (m

inut

es)

Com

pany

A

Com

pany

B

Com

pany

C

3.F

ind

the

slop

e of

th

e li

ne

for

Com

pan

yA

.Th

en i

nte

rpre

t th

is s

lope

as

a ra

te o

fch

ange

.0.

25;T

he

cost

of

a ca

llw

ith

Co

mp

any

A in

crea

ses

$0.2

5ea

ch m

in.

4.F

ind

the

slop

e of

th

e li

ne

for

Com

pan

y B

.Th

en i

nte

rpre

t th

is s

lope

as

a r

ate

of c

han

ge.

0.12

5;T

he

cost

of

a ca

ll w

ith

Co

mp

any

Bin

crea

ses

$0.1

25 e

ach

min

.

5.F

ind

the

slop

e of

th

e li

ne

for

Com

pan

yC

.Th

en i

nte

rpre

t th

is s

lope

as

a ra

te o

fch

ange

.0.

05;T

he

cost

of

a ca

llw

ith

Co

mp

any

C in

crea

ses

$0.0

5ea

ch m

in.

6.W

hic

h c

ompa

ny

char

ges

the

leas

t fo

rea

ch a

ddit

ion

al m

inu

te?

Exp

lain

you

rre

ason

ing.

Co

mp

any

C;

Co

mp

any

C c

har

ges

$0.

05 f

or

each

ad

dit

ion

al m

in,w

hile

Co

mp

anie

s A

an

d B

ch

arg

e $0

.25

and

$0.

125,

resp

ecti

vely

.


An

swer

s


Stud

y Gu

ide

and

Inte

rven

tion

So

lvin

g P

rop

ort

ion

s

©G

lenc

oe/M

cGra

w-H

ill20

0M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Det

erm

ine

wh

eth

er t

he

pai

r of

rat

ios

�2 20 4�an

d �1 12 8�

form

s a

pro

por

tion

.

Fin

d th

e cr

oss

prod

uct

s.

Sin

ce t

he

cros

s pr

odu

cts

are

not

equ

al,t

he

rati

os d

o n

ot f

orm

a p

ropo

rtio

n.

Sol

ve �1 32 0�

�� 7k 0�

.

�1 32 0��

� 7k 0�W

rite

the

equa

tion.

12 �

70�

30 �

kF

ind

the

cros

s pr

oduc

ts.

840

�30

kM

ultip

ly.

�8 34 00 ��

�3 30 0k �D

ivid

e ea

ch s

ide

by 3

0.

28�

kS

impl

ify.

Th

e so

luti

on i

s 28

.

Det

erm

ine

wh

eth

er e

ach

pai

r of

rat

ios

form

s a

pro

por

tion

.

1.�1 17 0�

, �1 52 �

no

2.�6 9�,

�1 12 8�ye

s3.

� 18 2�, �

1 10 5�ye

s

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E _

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ER

IOD

__

___

A p

rop

ort

ion

is a

n eq

uatio

n th

at s

tate

s th

at t

wo

ratio

s ar

e eq

uiva

lent

.To

dete

rmin

e w

heth

er a

pai

r of

ratio

s fo

rms

a pr

opor

tion,

use

cro

ss p

rodu

cts.

You

can

also

use

cro

ss p

rodu

cts

to s

olve

pro

port

ions

.

Lesson 4–3

©G

lenc

oe/M

cGra

w-H

ill19

9M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Ch

ien

-Sh

iun

g W

uA

mer

ican

ph

ysic

ist

Ch

ien

-Sh

iun

g W

u (

1912

–199

7) w

as

born

in

Sh

angh

ai,C

hin

a.In

193

6,sh

e ca

me

to t

he

Un

ited

S

tate

s to

fu

rth

er h

er s

tudi

es i

n s

cien

ce.S

he

rece

ived

her

do

ctor

ate

in p

hys

ics

in 1

940

from

th

e U

niv

ersi

ty o

f C

alif

orn

ia,a

nd

beca

me

know

n a

s on

e of

th

e w

orld

’s l

eadi

ng

phys

icis

ts.I

n 1

975,

she

was

aw

arde

d th

e N

atio

nal

Med

al

of S

cien

ce.

Wu

is

mos

t fa

mou

s fo

r an

exp

erim

ent

that

sh

e co

ndu

cted

in

195

7.T

he

outc

ome

of t

he

expe

rim

ent

was

con

side

red

the

mos

t si

gnif

ican

t di

scov

ery

in p

hys

ics

in m

ore

than

se

ven

ty y

ears

.Th

e ex

erci

se b

elow

wil

l h

elp

you

lea

rn s

ome

fact

s ab

out

it.

Th

e p

oin

ts g

iven

in

eac

h t

able

lie

on

a l

ine.

Fin

d t

he

slop

e of

th

e li

ne.

Th

e w

ord

or

ph

rase

fol

low

ing

the

solu

tion

wil

l co

mp

lete

th

est

atem

ent

corr

ectl

y.

1.2.

At

the

tim

e of

th

e ex

peri

men

t,W

uT

he

site

of

the

expe

rim

ent

was

th

e w

as a

pro

fess

or a

t .

in W

ash

ingt

on,D

.C.

slop

e �

3:C

olu

mbi

a U

niv

ersi

tysl

ope

�0:

Nat

ion

al B

ure

au o

f S

tan

dard

ssl

ope

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nfo

rd U

niv

ersi

tysl

ope

�3:

Sm

ith

son

ian

In

stit

uti

onC

olu

mb

ia U

niv

ersi

tyN

atio

nal

Bu

reau

of

Sta

nd

ard

s

3.4.

Th

e ex

peri

men

t in

volv

ed a

su

bsta

nce

In t

he

expe

rim

ent,

the

subs

tan

ce w

asca

lled

.

cool

ed t

o .

slop

e �

2:ca

rbon

14

slop

e �

�4 3�:�

273�

C

slop

e �

1:co

balt

60

slop

e �

�3 4�:�

100°

C

cob

alt

60�

273�

C

??

??

Enric

hmen

tN

AM

E__

____

____

____

____

____

____

____

____

____

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ATE

___

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PE

RIO

D

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47

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10



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tice:

Wor

d Pr

oble

ms

So

lvin

g P

rop

ort

ion

s

©G

lenc

oe/M

cGra

w-H

ill20

2M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

1.U

SAG

EA

12-

oun

ce b

ottl

e of

sh

ampo

ola

sts

En

riqu

e 16

wee

ks.H

ow l

ong

wou

ld y

ou e

xpec

t an

18-

oun

ce b

ottl

eof

th

e sa

me

bran

d to

las

t h

im?

24 w

k

2.C

OM

PUTE

RS

Abo

ut

13 o

ut

of 2

0 h

omes

hav

e a

pers

onal

com

pute

r.O

n a

str

eet

wit

h 6

0 h

omes

,how

man

y w

ould

you

expe

ct t

o h

ave

a pe

rson

al c

ompu

ter?

39 h

om

es

3.SN

AC

KS

A 6

-ou

nce

pac

kage

of

fru

itsn

acks

con

tain

s 45

pie

ces.

How

man

ypi

eces

wou

ld y

ou e

xpec

t in

a 1

0-ou

nce

pack

age?

75 p

iece

s

4.TY

PIN

GIn

grid

typ

es 3

pag

es i

n t

he

sam

e am

oun

t of

tim

e th

at T

anya

typ

es4.

5 pa

ges.

If I

ngr

id a

nd

Tan

ya s

tart

typi

ng

at t

he

sam

e ti

me,

how

man

ypa

ges

wil

l Tan

ya h

ave

type

d w

hen

Ingr

id h

as t

yped

11

page

s?16

.5 p

ages

5.SC

HO

OL

A g

radi

ng

mac

hin

e ca

n g

rade

48 m

ult

iple

-ch

oice

tes

ts i

n 1

min

ute

.H

ow l

ong

wil

l it

tak

e th

e m

ach

ine

togr

ade

300

test

s?6.

25 m

in

6.A

MU

SEM

ENT

PAR

KS

Th

e w

aiti

ng

tim

e to

ride

a r

olle

r co

aste

r is

20

min

ute

s w

hen

150

peop

le a

re i

n l

ine.

How

lon

g is

th

ew

aiti

ng

tim

e w

hen

240

peo

ple

are

inli

ne?

32 m

in

7.PR

OD

UC

TIO

NA

sh

op p

rodu

ces

39w

etsu

its

ever

y 2

wee

ks.

How

lon

g w

ill

it t

ake

the

shop

to

prod

uce

429

wet

suit

s?22

wk

8.FI

SHO

f th

e 50

fis

h t

hat

Jim

cau

ght

from

th

e la

ke,1

4 w

ere

trou

t.T

he

esti

mat

ed p

opu

lati

on o

f th

e la

ke i

s7,

500

fish

.Abo

ut

how

man

y tr

out

wou

ld y

ou e

xpec

t to

be

in t

he

lake

?2,

100

tro

ut

Prac

tice:

Ski

llsS

olv

ing

Pro

po

rtio

ns

Lesson 4–4

©G

lenc

oe/M

cGra

w-H

ill20

1M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Det

erm

ine

wh

eth

er e

ach

pai

r of

rat

ios

form

s a

pro

por

tion

.

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s

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ve e

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tion

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45

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___


An

swer

s


©G

lenc

oe/M

cGra

w-H

ill20

4M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Peo

ple

of

the

Un

ited

Sta

tes

A n

atio

nal

cen

sus

is t

aken

eve

ry t

en y

ears

.Th

e 19

90 c

ensu

s re

veal

ed t

hat

ther

e w

ere

abou

t 25

0,00

0,00

0 pe

ople

in

th

e U

nit

ed S

tate

s,an

d th

at a

bou

t 8

out

of 1

00 o

f th

ese

peop

le w

ere

5–13

yea

rs o

ld.T

o fi

nd

the

nu

mbe

r of

peop

le i

n t

he

Un

ited

Sta

tes

that

wer

e 5–

13 y

ears

old

,use

th

e ra

tio

ofpe

ople

5–1

3 ye

ars

old

and

crea

te a

pro

port

ion

.

� 18 00�� 25

0,0n 00

,000

�

To

solv

e th

e pr

opor

tion

,fin

d cr

oss

prod

uct

s.

8

250,

000,

000

�2,

000,

000,

000

and

n

100

�10

0n

Th

en d

ivid

e:2,

000,

000,

000

10

0�

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00.

In 1

990,

abou

t 20

,000

,000

peo

ple

in t

he

Un

ited

Sta

tes

wer

e 5–

13 y

ears

old

.

Use

th

e ap

pro

xim

ate

rati

os i

n e

ach

exe

rcis

e to

cre

ate

a p

rop

orti

on,

give

n t

hat

th

ere

wer

e ab

out

250,

000,

000

peo

ple

in

th

e U

nit

ed S

tate

s.T

hen

sol

ve a

nd

ch

oose

th

e co

rrec

t an

swer

fro

m t

he

choi

ces

at t

he

righ

t.

1.T

he

Un

ited

Sta

tes

is a

div

erse

col

lect

ion

of

diff

eren

t__

____

__A

.20

0,00

0,00

0ra

ces

and

eth

nic

ori

gin

s.A

sian

s or

Pac

ific

Isl

ande

rsac

cou

nte

d fo

r ab

out

� 13 00�of

th

e po

pula

tion

of

the

Un

ited

Sta

tes.

Abo

ut

how

man

y pe

ople

of A

sian

or

Pac

ific

-Isl

and

orig

in l

ived

in

th

e U

nit

ed S

tate

s?

2.A

fric

an-A

mer

ican

s ac

cou

nte

d fo

r ab

out

� 23 5�of

th

e__

____

__B

.22

,500

,000

popu

lati

on o

f th

e U

nit

ed S

tate

s.A

bou

t h

ow m

any

Afr

ican

-Am

eric

an p

eopl

e li

ved

in t

he

Un

ited

Sta

tes?

3.P

eopl

e of

His

pan

ic o

rigi

n a

ccou

nte

d fo

r ab

out

� 19 00�__

____

__C

.7,

500,

000

of t

he

popu

lati

on o

f th

e U

nit

ed S

tate

s.A

bou

t h

owm

any

peop

le o

f H

ispa

nic

ori

gin

liv

ed i

n t

he

Un

ited

Sta

tes?

4.C

auca

sian

peo

ple

acco

un

ted

for

abou

t �4 5�

of t

he

____

____

D.

2,00

0,00

0po

pula

tion

of

the

Un

ited

Sta

tes.

Abo

ut

how

man

ype

ople

of

wh

ite

or C

auca

sian

ori

gin

liv

ed i

n t

he

Un

ited

Sta

tes?

5.P

eopl

e of

Am

eric

an-I

ndi

an,E

skim

o,or

Alu

et o

rigi

n__

____

E.

30,0

00,0

00

acco

un

ted

for

abou

t � 1,

08 00�of

th

e po

pula

tion

of

the

Un

ited

Sta

tes.

Abo

ut

how

man

y pe

ople

of

Am

eric

an-I

ndi

an,E

skim

o,or

Alu

et o

rigi

n l

ived

in

the

Un

ited

Sta

tes?

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enric

hmen

t

C E B A D

Read

ing

to L

earn

Mat

hem

atic

sS

olv

ing

Pro

po

rtio

ns

Lesson 4–4

Pre-

Act

ivit

yR

ead

th

e in

tro

du

ctio

n a

t th

e to

p o

f p

age

170

in y

ou

r te

xtb

oo

k.W

rite

yo

ur

answ

ers

bel

ow

.

1.W

rite

a r

atio

th

at c

ompa

res

the

nu

mbe

r of

Cal

orie

s fr

om f

at t

o th

e to

tal

nu

mbe

r of

Cal

orie

s.W

rite

th

e ra

tio

as a

fra

ctio

n i

n s

impl

est

form

.

� 12 1�

2.S

upp

ose

you

pla

n t

o ea

t tw

o su

ch g

ran

ola

bars

.Wri

te a

rat

io c

ompa

rin

gth

e n

um

ber

of C

alor

ies

from

fat

to

the

tota

l n

um

ber

of C

alor

ies.

� 12 1�

3.Is

th

e ra

tio

of C

alor

ies

the

sam

e fo

r tw

o gr

anol

a ba

rs a

s it

is

for

one

gran

ola

bar?

Wh

y or

wh

y n

ot?

Th

e ra

tio

s ar

e eq

ual

bec

ause

mu

ltip

lyin

g t

he

nu

mer

ato

r an

d d

eno

min

ato

r o

f a

frac

tio

n b

yth

e sa

me

amo

un

t cr

eate

s an

eq

uiv

alen

t fr

acti

on

.

Rea

din

g t

he

Less

on

4.C

ompl

ete

the

sen

ten

ce:I

f tw

o ra

tios

for

m a

pro

port

ion

,th

en t

he

rati

osar

e sa

id t

o be

___

____

___.

pro

po

rtio

nal

5.D

o th

e ra

tios

�a b�an

d � dc �

alw

ays

form

a p

ropo

rtio

n?

Wh

y or

wh

y n

ot?

No

;S

amp

le a

nsw

er:T

he

rati

os

on

ly f

orm

a p

rop

ort

ion

if t

he

cro

ss p

rod

uct

s ad

and

bc

are

equ

al.

6.E

xpla

in h

ow y

ou c

an u

se c

ross

pro

duct

s to

sol

ve p

ropo

rtio

ns

in w

hic

h o

ne

of t

he

term

s is

not

kn

own

.S

amp

le a

nsw

er:

Fin

d t

he

cro

ssp

rod

uct

s,th

en d

ivid

e b

oth

sid

es o

f th

e eq

uat

ion

by

the

con

stan

t th

at is

mu

ltip

lied

by

the

un

kno

wn

var

iab

le.

Hel

pin

g Y

ou

Rem

emb

er7.

For

th

e pr

opor

tion

�a b�an

d � dc �,

wh

y do

you

th

ink

the

prod

uct

s ad

and

bcar

eca

lled

cro

ss p

rod

uct

s?S

amp

le a

nsw

er:

If y

ou

dra

w li

nes

fro

m a

to d

and

fro

m b

to c

in t

he

pro

po

rtio

n,t

he

lines

fo

rm a

cro

ss.

©G

lenc

oe/M

cGra

w-H

ill20

3M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___



©G

lenc

oe/M

cGra

w-H

ill20

6M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Det

erm

ine

wh

eth

er e

ach

pai

r of

pol

ygon

s is

sim

ilar

.Exp

lain

you

rre

ason

ing.

1.2.

Yes;

corr

esp

on

din

gN

o;

corr

esp

on

din

gan

gle

s ar

e co

ng

ruen

t an

dan

gle

s ar

e co

ng

ruen

t,bu

t

�1 10 5��

� 18 2��

�1 10 5��

� 18 2�.

�1 10 50 0��

�1 10 51 1�.

3.4.

Yes;

corr

esp

on

din

gYe

s;co

rres

po

nd

ing

ang

les

are

con

gru

ent

and

ang

les

are

con

gru

ent

and

�1 74 ��

�2 10 0��

�8 4�.�6 3�

�� 37 .5�

�� 37 .5�

.

5.6.

� 2x .6��

�8 4�;5.

2�6 x.5 �

��2 1. .6 8�

;4.

5

7.8.

� 1x .5��

� 36 .6�;

2.5

�1 x0 ��

� 96 .6�;

16

x

6

9.6

14

22.4

9.6

6

10

66.

5

1.5

3.6

3.9

x

x

1.8

2.6

6.5

88

2.6

44

x

67

7

3

3.5

3.5

208

1410

74

151

101

150

100

15

8

10

12

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice:

Ski

llsS

imila

r P

oly

go

ns

Lesson 4–5

Stud

y Gu

ide

and

Inte

rven

tion

Sim

ilar

Po

lyg

on

s

©G

lenc

oe/M

cGra

w-H

ill20

5M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Det

erm

ine

wh

eth

er �

AB

Cis

sim

ilar

to

�D

EF

.Exp

lain

you

r re

ason

ing.

�A

��

D,�

B �

�E

,�C

��

F,

� DAB E�

��4 6�

or �2 3�,

�B EC F�

��6 9�

or �2 3�,

� DAC F�

�� 18 2�

or �2 3�

Th

e co

rres

pon

din

g an

gles

are

con

gru

ent,

and

the

corr

espo

ndi

ng

side

s ar

e pr

opor

tion

al.

Th

us,

�A

BC

is s

imil

ar t

o �

DE

F.

Giv

en t

hat

pol

ygon

KL

MN

�p

olyg

on P

QR

S,w

rite

a p

rop

orti

on t

ofi

nd

th

e m

easu

re o

f P�

Q�.T

hen

sol

ve.

Th

e ra

tio

of c

orre

spon

din

g si

des

from

pol

ygon

KL

MN

topo

lygo

n P

QR

Sis

�4 3�.W

rite

a p

ropo

rtio

n w

ith

th

is s

cale

fact

or.L

et x

repr

esen

t th

e m

easu

re o

f P�

Q�.

� PKQL �

��4 3�

K�L�

corr

espo

nds

to P�

Q�.T

he s

cale

fact

or is

�4 3�.

�5 x��

�4 3�K

L�

5 an

d P

Q�

x

5�

3�

x �

4F

ind

the

cros

s pr

oduc

ts.

�1 45 ��

�4 4x �M

ultip

ly.T

hen

divi

de e

ach

side

by

4.

3.75

�x

Sim

plify

.

1.D

eter

min

e w

het

her

th

e po

lygo

ns

2.T

he

tria

ngl

es b

elow

are

sim

ilar

.Wri

te a

belo

w a

re s

imil

ar.E

xpla

in y

our

prop

orti

on t

o fi

nd

each

mis

sin

g m

easu

re.

reas

onin

g.T

hen

sol

ve.

No

;co

rres

po

nd

ing

an

gle

s�1 x5 �

��6 4�;

x�

10ar

e co

ng

ruen

t,bu

t

�1 12 1��

�5 4�.

1264 8

15x

11

5

124

Kx

3

5

N

LP

Q

SR

M

4

B

8

E

CA

DF

64

6

12

9

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Two

poly

gons

are

sim

ilar

if th

eir

corr

espo

ndin

g an

gles

are

con

grue

nt a

nd t

heir

corr

espo

ndin

g si

des

are

prop

ortio

nal.


An

swer

s


Pre-

Act

ivit

yC

om

ple

te t

he

Min

i Lab

at

the

top

of

pag

e 17

8 in

yo

ur

text

bo

ok.

Wri

te y

ou

r an

swer

s b

elo

w.

1.C

ompa

re t

he

angl

es o

f th

e tr

ian

gles

by

mat

chin

g th

em u

p.Id

enti

fy t

he

angl

e pa

irs

that

hav

e eq

ual

mea

sure

.m

�D

�m

�L

,m�

E�

m�

J,m

�F

�m

�K

2.E

xpre

ss t

he

rati

os �D L

KF �, �

E JKF �

,an

d �D L

E J�to

th

e n

eare

st t

enth

.0.

7;0.

7;0.

7

3.W

hat

do

you

not

ice

abou

t th

e ra

tios

of

the

mat

chin

g si

des

of m

atch

ing

tria

ngl

es?

Th

ey a

re a

pp

roxi

mat

ely

equ

al.

Rea

din

g t

he

Less

on

4.C

ompl

ete

the

sen

ten

ce:I

f tw

o po

lygo

ns

are

sim

ilar

,th

en t

hei

rco

rres

pon

din

g an

gles

are

___

____

___,

and

thei

r co

rres

pon

din

g si

des

are

____

____

__.

con

gru

ent;

pro

po

rtio

nal

5.If

tw

o po

lygo

ns

hav

e co

rres

pon

din

g an

gles

th

at a

re c

ongr

uen

t,do

es t

hat

mea

n t

hat

th

e po

lygo

ns

are

sim

ilar

? W

hy

or w

hy

not

?S

amp

lean

swer

:N

o;

the

po

lyg

on

s ar

e si

mila

r o

nly

if t

hei

rco

rres

po

nd

ing

sid

es a

re p

rop

ort

ion

al.

6.If

th

e si

des

of o

ne

squ

are

are

3 ce

nti

met

ers

and

the

side

s of

an

oth

ersq

uar

e ar

e 9

cen

tim

eter

s,w

hat

is

the

rati

o of

cor

resp

ondi

ng

side

s fr

om

the

firs

t sq

uar

e to

th

e se

con

d sq

uar

e?�1 3�

Hel

pin

g Y

ou

Rem

emb

er7.

Loo

k u

p th

e ev

eryd

ay d

efin

itio

n o

f th

e w

ord

sim

ilar

in a

dic

tion

ary.

How

does

th

e de

fin

itio

n r

elat

e to

wh

at y

ou l

earn

ed i

n t

his

les

son

?S

amp

lean

swer

:Th

e w

ord

sim

ilar

mea

ns

hav

ing

ch

arac

teri

stic

s in

com

mo

n;

sim

ilar

po

lyg

on

s h

ave

con

gru

ent

ang

les

inco

mm

on

an

d p

rop

ort

ion

al s

ides

in c

om

mo

n.

Read

ing

to L

earn

Mat

hem

atic

sS

imila

r P

oly

go

ns

©G

lenc

oe/M

cGra

w-H

ill20

8M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice:

Wor

d Pr

oble

ms

Sim

ilar

Po

lyg

on

s

Lesson 4–5

©G

lenc

oe/M

cGra

w-H

ill20

7M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

1.JO

UR

NA

LISM

Th

e ed

itor

of

the

sch

ool

new

spap

er m

ust

red

uce

th

e si

ze o

f a

grap

h t

o fi

t in

on

e co

lum

n.T

he

orig

inal

grap

h i

s 2

inch

es b

y 2

inch

es,a

nd

the

scal

e fa

ctor

fro

m t

he

orig

inal

to

the

redu

ced

grap

h i

s 8:

3.F

ind

the

dim

ensi

ons

of t

he

grap

h a

s it

wil

lap

pear

in

on

e co

lum

n o

f th

e n

ewsp

aper

.

�3 4�in

.by

�3 4�in

.

2.PH

OTO

CO

PIES

Lyd

ia p

lan

s to

use

aph

otoc

opy

mac

hin

e to

in

crea

se t

he

size

of a

sm

all

char

t th

at s

he

has

mad

e as

part

of

her

sci

ence

pro

ject

.Th

e or

igin

alch

art

is 4

in

ches

by

5 in

ches

.If

she

use

s a

scal

e fa

ctor

of

5:11

,wil

l th

ech

art

fit

on a

sh

eet

of p

aper

8�1 2�

inch

esby

11

inch

es?

Exp

lain

.

No

;it

will

be

8 �4 5�

in.b

y 11

in.

3.M

ICR

OC

HIP

ST

he

imag

e of

a m

icro

chip

in a

pro

ject

ion

mic

rosc

ope

mea

sure

s 8

inch

es b

y 10

in

ches

.Th

e w

idth

of

the

actu

al c

hip

is

4 m

illi

met

ers.

How

lon

gis

th

e ch

ip?

5 m

m

4.PR

OJE

CTI

ON

SA

dra

win

g on

atr

ansp

aren

cy i

s 11

.25

cen

tim

eter

s w

ide

by 2

3.5

cen

tim

eter

s ta

ll.T

he

wid

th o

fth

e im

age

of d

raw

ing

proj

ecte

d on

to a

scre

en i

s 2.

7 m

eter

s.H

ow t

all

is t

he

draw

ing

on t

he

scre

en?

5.64

m

5.G

EOM

ETRY

Pol

ygon

AB

CD

is s

imil

ar t

opo

lygo

n F

GH

I.E

ach

sid

e of

pol

ygon

AB

CD

is 3

�1 4�ti

mes

lon

ger

than

th

eco

rres

pon

din

g si

de o

f po

lygo

n F

GH

I.F

ind

the

peri

met

er o

f po

lygo

n F

GH

I.

42�1 4�

in.

6.K

ITES

A t

oy c

ompa

ny

prod

uce

s tw

oki

tes

wh

ose

shap

es a

re g

eom

etri

call

ysi

mil

ar.F

ind

the

len

gth

of

the

mis

sin

gsi

de o

f th

e sm

alle

r ki

te.

18.7

5 in

.25

in.

25 in

.

30 in

.22

.5 in

.

30 in

.x

B

A

D

I

H

F

G

C

3 in

.

2 in

. 5 in

.

3 in

.



Stud

y Gu

ide

and

Inte

rven

tion

Sca

le D

raw

ing

s an

d M

od

els

©G

lenc

oe/M

cGra

w-H

ill21

0M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

INTE

RIO

R D

ESIG

NA

des

ign

er h

as m

ade

asc

ale

dra

win

g of

a l

ivin

g ro

om f

or o

ne

of h

er c

lien

ts.T

he

scal

e of

th

e d

raw

ing

is 1

in

ch �

1 �1 3�

feet

.On

th

e d

raw

ing,

the

sofa

is

6 in

ches

lon

g.F

ind

th

e ac

tual

len

gth

of

the

sofa

.

Let

xre

pres

ent

the

actu

al l

engt

h o

f th

e so

fa.W

rite

an

d so

lve

a pr

opor

tion

.

Th

e ac

tual

len

gth

of

the

sofa

is

8 fe

et.

Fin

d t

he

scal

e fa

ctor

for

th

e d

raw

ing

in E

xam

ple

1.

Wri

te t

he

rati

o of

1 i

nch

to

1 �1 3�

feet

in

sim

ples

t fo

rm.

�� 11 6i in n.

�.

��C

onve

rt 1

�1 3�fe

et t

o in

ches

.

Th

e sc

ale

fact

or i

s � 11 6�

or 1

:16.

Th

is m

ean

s th

at e

ach

dis

tan

ce o

n t

he

draw

ing

is � 11 6�

the

actu

al d

ista

nce

.

LAN

DSC

API

NG

Yu

tak

a h

as m

ade

a sc

ale

dra

win

gof

his

yar

d.T

he

scal

e of

th

e d

raw

ing

is1

cen

tim

eter

= 0

.5 m

eter

.

1.T

he

len

gth

of

the

pati

o is

4.5

cen

tim

eter

s in

th

edr

awin

g.F

ind

the

actu

al l

engt

h.

2.25

m2.

Th

e ac

tual

dis

tan

ce b

etw

een

th

e w

ater

fau

cet

and

the

pear

tre

e is

11.

2 m

eter

s.F

ind

the

corr

espo

ndi

ng

dist

ance

on

th

e dr

awin

g.22

.4 c

m3.

Fin

d th

e sc

ale

fact

or f

or t

he

draw

ing.

� 51 0�

1 in

.� 1 �

1 3�ft

To f

ind

the

scal

e fa

ctor

for

scal

e dr

awin

gs a

nd m

odel

s, w

rite

the

ratio

giv

en b

y th

e sc

ale

in s

impl

est

form

.

1 in

.6

in.

1 f

t1 3

x ft

�

1 · x

� 1

· 6

1 3x

� 8

draw

ing

dist

ance

→

actu

al d

ista

nce

→

← d

raw

ing

leng

th←

act

ual l

engt

h

Fin

d th

e cr

oss

prod

ucts

.

Sim

plify

.

↓↓

Dra

win

g S

cale

Act

ual L

engt

h

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

1 in

. = 1

ft

Sofa

1 3

1 cm

= 0

.5 m

Patio

Pond

Path

Wat

er F

auce

t

Pear

Tree

Gard

en

Dis

tanc

es o

n a

scal

e dr

awin

g or

mod

el a

re p

ropo

rtio

nal t

o re

al-li

fe d

ista

nces

.The

sca

leis

det

erm

ined

by t

he r

atio

of

a gi

ven

leng

th o

n a

draw

ing

or m

odel

to

its c

orre

spon

ding

act

ual l

engt

h.

Lesson 4–5

©G

lenc

oe/M

cGra

w-H

ill20

9M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Sim

ilar

and

Co

ng

ruen

t Fi

gu

res

If a

4-i

nch

by

5-in

ch p

hot

ogra

ph i

s en

larg

ed t

o an

8-i

nch

by

10-i

nch

phot

ogra

ph,t

he

phot

ogra

phs

are

said

to

be s

imil

ar.T

hey

hav

e th

e sa

me

shap

e,bu

t th

ey d

o n

ot h

ave

the

sam

e si

ze.I

f a

4-in

ch b

y 5-

inch

ph

otog

raph

is d

upl

icat

ed a

nd

a n

ew 4

-in

ch b

y 5-

inch

ph

otog

raph

is

mad

e,th

eph

otog

raph

s ar

e sa

id t

o be

con

gru

ent.

Th

ey h

ave

the

sam

e si

ze a

nd

shap

e.

In e

ach

exe

rcis

e,id

enti

fy w

hic

h o

f th

e tr

ian

gles

are

con

gru

ent

toea

ch o

ther

an

d i

den

tify

wh

ich

of

the

shap

es a

re s

imil

ar t

o ea

ch o

ther

.U

se t

he

sym

bol

for

�co

ngr

uen

ce a

nd

th

esy

mb

ol�

for

sim

ilar

ity.

1.2.

a�

b;

a �

b;

c�

db

�c;

a �

c

3.4.

AB

H �

LK

C;

CD

P �

MN

P;

QR

T �

MN

P;

QR

T �

CD

PB

CG

�JK

M;

AQ

H �

LH

Q;

BT

D �

BC

G;

AB

D �

CB

D;

HK

J �

NM

L;

JKM

�JN

P;

HK

J �

AB

D;

HK

J �

CB

D;

BT

D �

JNP

;L

MN

�D

BC

;L

MN

�D

BA

BC

G �

JNP

;B

TD

�JK

M

5.

AD

C �

HK

J;A

DC

�A

BD

;A

DC

�C

BD

;A

DC

�L

MN

;A

DC

�D

BC

;A

DC

�D

BA

Enric

hmen

tN

AM

E__

____

____

____

____

____

____

____

____

____

__D

ATE

___

____

____

___

PE

RIO

D

____

_

a

b

cd

f

a

bc

d

AB

C

DJ

L

HN

KM

AB

CD

HK

LM

N

P

Q RT

AB

T C

D

Q

G

H J

LK

M

NP


An

swer

s


Prac

tice:

Wor

d Pr

oble

ms

Sca

le D

raw

ing

s an

d M

od

els

©G

lenc

oe/M

cGra

w-H

ill21

2M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

CA

MPU

S PL

AN

NIN

GF

or E

xerc

ises

1–3

,use

th

efo

llow

ing

info

rmat

ion

.

Th

e lo

cal

sch

ool

dist

rict

has

mad

e a

scal

e m

odel

of t

he

cam

pus

of E

nge

ls M

iddl

e S

choo

l in

clu

din

ga

prop

osed

new

bu

ildi

ng.

Th

e sc

ale

of t

he

mod

elis

1 i

nch

�3

feet

.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

1.A

n e

xist

ing

gym

nas

ium

is

8 in

ches

tal

lin

th

e m

odel

.How

tal

l is

th

e ac

tual

gym

nas

ium

?24

ft

2.T

he

new

bu

ildi

ng

is 2

2.5

inch

es f

rom

the

gym

nas

ium

in

th

e m

odel

.Wh

atw

ill

be t

he

actu

al d

ista

nce

fro

m t

he

gym

nas

ium

to

the

new

bu

ildi

ng

if i

tis

bu

ilt?

67.5

ft

3.W

hat

is

the

scal

e fa

ctor

of

the

mod

el?

� 31 6�

4.M

APS

On

a m

ap,t

wo

citi

es a

re 5

�3 4�

inch

es a

part

.Th

e sc

ale

of t

he

map

is

�1 2�in

ch �

3 m

iles

.Wh

at i

s th

e ac

tual

dist

ance

bet

wee

n t

he

tow

ns?

34�1 2�

mi

5.TR

UC

KS

Th

e be

d of

Jer

ry’s

pic

kup

tru

ckis

6 f

eet

lon

g.O

n a

sca

le m

odel

of

the

tru

ck,t

he

bed

is 8

in

ches

lon

g.W

hat

is

the

scal

e of

th

e m

odel

?

1 in

.��3 4�

ft

6 ft

6.H

OU

SIN

GM

arta

is

mak

ing

a sc

ale

draw

ing

of h

er a

part

men

t fo

r a

sch

ool

proj

ect.

Th

e ap

artm

ent

is 2

8 fe

et w

ide.

On

her

dra

win

g,th

e ap

artm

ent

is

7 in

ches

wid

e.W

hat

is

the

scal

e of

Mar

ta’s

dra

win

g?1

in.�

4 ft

28 ft

Gymnasium

Parking

Acad

emic

Build

ing

View

of C

ampu

s fro

m A

bove

New

Build

ing

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tice:

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llsS

cale

Dra

win

gs

and

Mo

del

s

Lesson 4–6

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w-H

ill21

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athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

AR

CH

ITEC

TUR

ET

he

scal

e on

a s

et o

f ar

chit

ectu

ral

dra

win

gs f

or a

hou

seis

1.5

in

ches

�2

feet

.Fin

d t

he

len

gth

of

each

par

t of

th

e h

ouse

.

7.W

hat

is

the

scal

e fa

ctor

of

thes

e dr

awin

gs?

� 11 6�

TOW

N P

LAN

NIN

GF

or E

xerc

ises

8–1

1,u

se t

he

foll

owin

g in

form

atio

n.

As

par

t of

a d

own

tow

n r

enew

al p

roje

ct,b

usi

nes

ses

hav

e co

nst

ruct

eda

scal

e m

odel

of

the

tow

n s

qu

are

to p

rese

nt

to t

he

city

com

mis

sion

for

its

app

rova

l.T

he

scal

e of

th

e m

odel

is

1 in

ch �

7 fe

et.

8.T

he

cou

rth

ouse

is

the

tall

est

buil

din

g in

th

e to

wn

squ

are.

If i

t is

5 �1 2�

inch

es t

all

in t

he

mod

el,h

ow t

all

is t

he

actu

al b

uil

din

g?

38�1 2�

ft

9.T

he

busi

nes

s ow

ner

s w

ould

lik

e to

in

stal

l n

ew l

ampp

osts

th

at a

reea

ch 1

2 fe

et t

all.

How

tal

l ar

e th

e la

mpp

osts

in

th

e m

odel

?

1 �5 7�

in.

10.

In t

he

mod

el,t

he

lam

ppos

ts a

re 3

�3 7�in

ches

apa

rt.H

ow f

ar a

part

wil

l th

ey b

e w

hen

th

ey a

re i

nst

alle

d?24

ft

11.

Wh

at i

s th

e sc

ale

fact

or?

� 81 4�

12.

MA

PSO

n a

map

,tw

o ci

ties

are

6�1 2�

inch

es a

part

.Th

e ac

tual

dis

tan

cebe

twee

n t

he

citi

es i

s 10

4 m

iles

.Wh

at i

s th

e sc

ale

of t

he

map

?1

in.�

16 m

i

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

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_P

ER

IOD

__

___

Roo

mD

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all

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.5 f

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ft



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athe

mat

ics:

App

licat

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Con

cept

s, C

ours

e 3

Scal

e D

raw

ing

sT

he

figu

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t th

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ght

has

an

are

a of

6 s

quar

e u

nit

s.If

th

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gure

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ted

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ap,a

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was

dra

wn

to

a sc

ale

of 1

un

it �

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he

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th

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wou

ld b

e 6

ft a

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the

figu

re w

ould

repr

esen

t an

are

a of

54

squ

are

feet

.

Th

e ra

tio

of t

he

actu

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rea

of t

he

figu

re t

o th

e sc

ale

area

of

the

figu

re c

an b

e ex

pres

sed

as a

rat

io.

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or 1

to

9

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rea

and

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e sc

ale

area

of

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e fi

gure

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hen

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ine

the

rati

o of

act

ual

are

a to

sca

le a

rea.

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cale

:1 u

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00

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tual

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ea

768

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4,32

0

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o 1

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4ra

tio

1 to

144

5.S

cale

:1 u

nit

�18

in

.6.

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le:1

un

it �

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actu

al a

rea

10ac

tual

are

a 24

scal

e ar

ea3,

240

scal

e ar

ea

864

rati

o 1

to 3

24ra

tio

1 to

36

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enric

hmen

t

Pre-

Act

ivit

yR

ead

th

e in

tro

du

ctio

n a

t th

e to

p o

f p

age

184

in y

ou

r te

xtb

oo

k.W

rite

yo

ur

answ

ers

bel

ow

.

1.H

ow m

any

un

its

wid

e is

th

e ro

om?

9

2.T

he

actu

al w

idth

of

the

room

is

18 f

eet.

Wri

te a

rat

io c

ompa

rin

g th

edr

awin

g w

idth

to

the

actu

al w

idth

.9

un

its:

18 f

eet

3.S

impl

ify

the

rati

o yo

u f

oun

d an

d co

mpa

re i

t to

th

e sc

ale

show

n a

t th

ebo

ttom

of

the

draw

ing.

2,3.

Bo

th t

he

rati

o a

nd

th

e sc

ale

ind

icat

e th

at 1

un

it o

n t

he

dra

win

g is

eq

ual

to

2 f

eet

inre

alit

y.

Rea

din

g t

he

Less

on

4.G

ive

anot

her

exa

mpl

e of

a s

cale

dra

win

g or

sca

le m

odel

th

at i

s di

ffer

ent

from

th

e ex

ampl

es o

f sc

ale

draw

ings

an

d sc

ale

mod

els

give

n o

n p

ages

184–

185

in y

our

text

book

.S

amp

le a

nsw

er:

scal

e m

od

els

of

build

ing

s

5.C

ompl

ete

the

sen

ten

ce:d

ista

nce

s on

a s

cale

mod

el a

re _

____

____

_ to

dist

ance

s in

rea

l li

fe.

pro

po

rtio

nal

6.W

hat

is

the

scal

e fa

ctor

for

a m

odel

if

part

of

the

mod

el t

hat

is

4 in

ches

corr

espo

nds

to

a re

al-l

ife

obje

ct t

hat

is

16 i

nch

es?

�1 4�

Hel

pin

g Y

ou

Rem

emb

er7.

Mak

e a

scal

e dr

awin

g of

a r

oom

,su

ch a

s yo

ur

clas

sroo

m o

r yo

ur

bedr

oom

.S

elec

t an

app

ropr

iate

sca

le s

o th

at y

our

draw

ing

is a

rea

son

able

siz

e.B

esu

re t

o in

dica

te y

our

scal

e on

you

r dr

awin

g.U

se a

not

her

pie

ce o

f pa

per

ifn

eces

sary

.S

ee s

tud

ents

’wo

rk.

Read

ing

to L

earn

Mat

hem

atic

sS

cale

Dra

win

gs

and

Mo

del

s

Lesson 4–6

©G

lenc

oe/M

cGra

w-H

ill21

3M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___


An

swer

s


Prac

tice:

Ski

llsIn

dir

ect

Mea

sure

men

t

©G

lenc

oe/M

cGra

w-H

ill21

6M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Wri

te a

pro

por

tion

an

d s

olve

th

e p

rob

lem

.

1.H

EIG

HT

How

tal

l is

Bec

ky?

2.FL

AG

SH

ow t

all

is t

he

flag

pole

?

�h 3��

�7 4�;5 �

1 4�ft

�;

22�3 4�

ft

3.B

EAC

HH

ow d

eep

is t

he

wat

er

4.A

CC

ESSI

BIL

ITY

How

hig

h i

s th

e ra

mp

50 f

eet

from

sh

ore?

wh

en i

t is

2 f

eet

from

th

e bu

ildi

ng?

(Hin

t:�

AB

E�

�A

CD

)

�h 1��

�5 80 �;

6.25

ft

� 2h .5��

�1 28 0�;

2.25

ft

5.A

MU

SEM

ENT

PAR

KS

Th

e tr

ian

gles

in

6.C

LASS

CH

AN

GES

Th

e tr

ian

gles

in

th

e fi

gure

the

figu

re a

re s

imil

ar.H

ow f

ar i

s th

ear

e si

mil

ar.H

ow f

ar i

s th

e en

tran

ce t

ow

ater

rid

e fr

om t

he

roll

er c

oast

er?

the

gym

nas

ium

fro

m t

he

ban

d ro

om?

Rou

nd

to t

he

nea

rest

ten

th.

� 1d 0��

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�21

.4 m

� 3d 2��

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38.4

m

45 m

Info

rmat

ion

Boot

h

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er R

ide

Ferr

is W

heel

Rolle

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ster

Park

Ent

ranc

e21

m10

md

m

30 m

25 m

Tenn

is C

ourt

Band

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m

Gym

nasi

um Cafe

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Foun

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32 m

d m

2 ft

h ft

A

BC

DE

20 ft

2.5

fth

ft

50 ft

8 ft

1 ft

31�1 2�

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h � 6 �1 2�

9 ft

h ft

6ft

1 2

31ft

1 2

7 ft

3 ft

h ft

4 ft

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Lesson 4–7

©G

lenc

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cGra

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ill21

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athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

LIG

HTI

NG

Geo

rge

is s

tan

din

g n

ext

to a

ligh

tpol

e in

th

e m

idd

le o

f th

e d

ay.G

eorg

e’s

shad

ow i

s 1.

5 fe

et l

ong,

and

th

e li

ghtp

ole’

s sh

adow

is

4.5

feet

lon

g.If

Geo

rge

is 6

fee

t ta

ll,h

ow t

all

is t

he

ligh

tpol

e?

Wri

te a

pro

port

ion

an

d so

lve.

Geo

rge’

s sh

adow

→1.

56

Geo

rge’

s he

ight

light

pole

’s s

hado

w→

4.5

hlig

htpo

le’s

hei

ght

1.5

�h

�4.

5 �

6F

ind

the

cros

s pr

oduc

ts.

1.5h

�27

Mul

tiply

.

�1 1.5 .5h ��

� 12 .7 5�D

ivid

e ea

ch s

ide

by 1

.5.

h�

18S

impl

ify.

Th

e li

ghtp

ole

is 1

8 fe

et t

all.

1.M

ON

UM

ENTS

A s

tatu

e ca

sts

a sh

adow

30

feet

lo

ng.

At

the

sam

e ti

me,

a pe

rson

wh

o is

5 f

eet

tall

cas

ts a

sh

adow

th

at i

s 6

feet

lon

g.H

ow

tall

is

the

stat

ue?

25 f

t

2.B

UIL

DIN

GS

A b

uil

din

g ca

sts

a sh

adow

72

met

ers

lon

g.A

t th

e sa

me

tim

e,a

perk

ing

met

er t

hat

is

1.2

met

ers

tall

cas

ts a

sh

adow

th

at i

s 0.

8 m

eter

lo

ng.

How

tal

l is

th

e bu

ildi

ng?

108

m

3.SU

RV

EYIN

GT

he

two

tria

ngl

es s

how

n i

n t

he

figu

re a

re s

imil

ar.F

ind

the

dist

ance

dac

ross

R

ed R

iver

.2m

1 m

.9 m

1.8

m

Red

Rive

rd

h ft

72 m

1.2

m

0.8

m

h ft

30 ft

5 ft

6 ft

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Ind

irec

t M

easu

rem

ent

Dis

tanc

es o

r le

ngth

s th

at a

re d

iffic

ult

to m

easu

re d

irect

ly c

an s

omet

imes

be

foun

d us

ing

the

prop

ertie

sof

sim

ilar

poly

gons

and

pro

port

ions

.Thi

s ki

nd o

f m

easu

rem

ent

is c

alle

d in

dir

ect

mea

sure

men

t.

h ft

6 ft

4ft

1 21

ft1 2

→→

�



©G

lenc

oe/M

cGra

w-H

ill21

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athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Pre-

Act

ivit

yR

ead

th

e in

tro

du

ctio

n a

t th

e to

p o

f p

age

188

in y

ou

r te

xtb

oo

k.W

rite

yo

ur

answ

ers

bel

ow

.

1.H

ow i

s th

e ca

vem

an m

easu

rin

g th

e di

stan

ce t

o th

e S

un

?H

e is

mea

suri

ng

th

e d

ista

nce

as

if it

wer

e a

flat

su

rfac

e d

irec

tly

infr

on

t o

f h

im.

Rea

din

g t

he

Less

on

2.C

ompl

ete

the

foll

owin

g se

nte

nce

.W

hen

you

sol

ve a

pro

blem

usi

ng

shad

ow r

ecko

nin

g,th

e ob

ject

s be

ing

com

pare

d an

d th

eir

shad

ows

form

tw

o si

des

of _

____

____

____

__.

sim

ilar

tria

ng

les

3.S

upp

ose

that

you

are

sta

ndi

ng

nea

r a

buil

din

g an

d yo

u s

ee t

he

shad

ows

cast

by

you

an

d th

e bu

ildi

ng.

If y

ou k

now

th

e le

ngt

h o

f ea

ch o

f th

ese

shad

ows

and

you

kn

ow h

ow t

all

you

are

,wri

te a

pro

port

ion

in

wor

ds t

hat

you

can

use

to

fin

d th

e h

eigh

t of

th

e bu

ildi

ng.

Sam

ple

an

swer

:

�

4.ST

ATU

EIf

a s

tatu

e ca

sts

a 6-

foot

sh

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an

d a

5-fo

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ailb

ox c

asts

a4-

foot

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,how

tal

l is

th

e st

atu

e?7.

5 ft

Hel

pin

g Y

ou

Rem

emb

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Wor

k w

ith

a p

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er.H

ave

you

r pa

rtn

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raw

tw

o tr

ian

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th

at a

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ith

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onal

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e la

bele

d.T

ell

you

r pa

rtn

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ow t

o w

rite

apr

opor

tion

to

solv

e fo

r th

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ngt

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f th

e si

de c

orre

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din

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th

ead

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onal

sid

e la

bele

d.S

ee s

tud

ents

’wo

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hei

gh

t o

f th

e bu

ildin

g�

��

my

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hem

atic

sIn

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lenc

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cGra

w-H

ill21

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athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Lesson X–1

Prac

tice:

Wor

d Pr

oble

ms

Ind

irec

t M

easu

rem

ent

Lesson 4–7

1.H

EIG

HT

Pac

o is

6 f

eet

tall

an

d ca

sts

a12

-foo

t sh

adow

.At

the

sam

e ti

me,

Dia

ne

cast

s an

11-

foot

sh

adow

.How

tal

lis

Dia

ne?

5 �1 2�

ft

2.LI

GH

TIN

GIf

a 2

5-fo

ot-t

all

hou

se c

asts

a75

-foo

t sh

adow

at

the

sam

e ti

me

that

ast

reet

ligh

t ca

sts

a 60

-foo

t sh

adow

,how

tall

is

the

stre

etli

ght?

20 f

t

3.FL

AG

POLE

Len

a is

5�1 2�

feet

tal

l an

d ca

sts

an 8

-foo

t sh

adow

.At

the

sam

e ti

me,

afl

agpo

le c

asts

a 4

8-fo

ot s

had

ow.H

owta

ll i

s th

e fl

agpo

le?

33 f

t

4.LA

ND

MA

RK

SA

wom

an w

ho

is 5

fee

t5

inch

es t

all

is s

tan

din

g n

ear

the

Spa

ce N

eedl

e in

Sea

ttle

,Was

hin

gton

;sh

e ca

sts

a 13

-in

ch s

had

ow a

t th

e sa

me

tim

e th

at t

he

Spa

ce N

eedl

e ca

sts

a12

1-fo

ot s

had

ow.H

ow t

all

is t

he

Spa

ceN

eedl

e?61

4 ft

5.N

ATI

ON

AL

MO

NU

MEN

TSA

42-

foot

flag

pole

nea

r th

e W

ash

ingt

onM

onu

men

t ca

sts

a sh

adow

th

at i

s14

fee

t lo

ng.

At

the

sam

e ti

me,

the

Was

hin

gton

Mon

um

ent

cast

s a

shad

owth

at i

s 18

5 fe

et l

ong.

How

tal

l is

th

eW

ash

ingt

on M

onu

men

t?55

5 ft

6.A

CC

ESSI

BIL

ITY

A r

amp

slop

es u

pwar

dfr

om t

he

side

wal

k to

th

e en

tran

ce o

f a

buil

din

g at

a c

onst

ant

incl

ine.

If t

he

ram

p is

2 f

eet

hig

h w

hen

it

is 5

fee

tfr

om t

he

side

wal

k,h

ow h

igh

is

the

ram

p w

hen

it

is 7

fee

t fr

om t

he

side

wal

k?2.

8 ft

5 ft

2 ft


An

swer

s


©G

lenc

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athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Gra

ph

�A

BC

wit

h v

erti

ces

A(�

2,�

1),

B(2

,3),

and

C(2

,�1)

.Th

en g

rap

h i

ts

imag

e �

A�B

�C�a

fter

a d

ilat

ion

wit

h a

scal

e fa

ctor

of

�3 2�.

A(�

2,�

1)→

��2

��3 2�,

�1

��3 2� �

→A

� ��3,

��3 2� �

B(2

,3)

→�2

��3 2�,

3 �

�3 2� �→

B� �3

,4�1 2� �

C(2

,�1)

→�2

��3 2�,

�1

��3 2� �

→C

� �3,�

�3 2� �S

egm

ent

M�N

�is

a d

ilat

ion

of

segm

ent

MN

.Fin

d t

he

scal

e fa

ctor

of

the

dil

atio

n a

nd

cla

ssif

y it

as

an e

nla

rgem

ent

or a

red

uct

ion

.

Wri

te t

he

rati

o of

th

e x-

or

y-co

ordi

nat

e of

on

e ve

rtex

of

the

dila

ted

figu

re t

o th

e x-

or

y-co

ordi

nat

e of

th

e co

rres

pon

din

gve

rtex

of

the

orig

inal

fig

ure

.Use

th

e x-

coor

din

ates

of

N(1

,�2)

and

N�(

2,�

4).

��2 1�

or 2

Th

e sc

ale

fact

or i

s 2.

Sin

ce t

he

imag

e is

lar

ger

than

th

e or

igin

alfi

gure

,th

e di

lati

on i

s an

en

larg

emen

t.

1.P

olyg

on A

BC

Dh

as v

erti

ces

A(2

,4),

B(�

1,5)

,C(�

3,�

5),a

nd

D(3

,�4)

.Fin

d th

e co

ordi

nat

es o

f it

s im

age

afte

r a

dila

tion

wit

h a

sca

le f

acto

r of

�1 2�.T

hen

gra

ph p

olyg

on A

BC

Dan

d it

s

dila

tion

.

A�(

1,2)

,B� ��

�1 2�,2 �

1 2� �,C

� ��3 2�,

�2 �

1 2� �,D

� �1�1 2�,

�2 �

2.S

egm

ent

P�Q

�is

a d

ilat

ion

of

segm

ent

PQ

.Fin

d th

e sc

ale

fact

or o

f th

e di

lati

on a

nd

clas

sify

it

as a

n e

nla

rgem

ent

or a

redu

ctio

n.

�2 3�;re

du

ctio

n

x-co

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nat

e of

poi

nt

N�

��

�x-

coor

din

ate

of p

oin

t N

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Dila

tio

ns

The

imag

e pr

oduc

ed b

y en

larg

ing

or r

educ

ing

a fig

ure

is c

alle

d a

dila

tio

n.

y

xO

A�

C

B

B�

C�

A

y

xO

M�

M

N

N�

y

xOB�

AB

CC

�

A�

D�

D

y

xO

PP

�

Q�

Q

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athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Ind

irec

t M

easu

rem

ent

A p

ropo

rtio

n c

an b

e u

sed

to d

eter

min

e th

e h

eigh

tof

tal

l st

ruct

ure

s if

th

ree

vari

able

s of

th

e pr

opor

tion

are

know

n.T

he

thre

e kn

own

var

iabl

es a

re u

sual

lyth

e h

eigh

t a

of t

he

obse

rver

,th

e le

ngt

h b

of t

he

obse

rver

’s s

had

ow,a

nd

the

len

gth

dof

th

est

ruct

ure

’s s

had

ow.H

owev

er,a

pro

port

ion

can

be

solv

ed g

iven

an

y th

ree

of t

he

fou

r va

riab

les.

Th

is c

har

t co

nta

ins

info

rmat

ion

ab

out

vari

ous

obse

rver

s an

d t

all

bu

ild

ings

.Use

pro

por

tion

s an

d y

our

calc

ula

tor

to c

omp

lete

th

e ch

art

of t

all

bu

ild

ings

of

the

wor

ld.

Enric

hmen

tN

AM

E__

____

____

____

____

____

____

____

____

____

__D

ATE

___

____

____

___

PE

RIO

D

____

_

Lesson X–1 Lesson 4–7

a

b

c

d

a bc d

�

Hei

ght

ofO

bse

rver

Len

gth

of

Sh

adow

Bu

ild

ing

Loc

atio

nH

eigh

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ild

ing

Len

gth

of

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adow

1.5

ft8

in.

Nat

wes

t,L

ondo

n60

0 ft

80 f

t

2.4

ft 9

in

.19

in.

Col

um

bia

Sea

firs

tC

ente

r,S

eatt

le95

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318

ft

3.5

ft 1

0 in

.14

in

.W

ach

ovia

Bu

ildi

ng,

Win

ston

-Sal

em41

0 ft

82 f

t

4.6

ft15

in

.W

ater

fron

t T

ower

s,H

onol

ulu

400

ft83

ft

4 in

.

5.6

ft1

ftC

N T

ower

,T

oron

to1,

821

ft30

3 ft

6 i

n.

6.5

ft 9

in

.1

ft 1

1 in

.G

atew

ay A

rch

,S

t.L

ouis

630

ft21

0 ft

7.5

ft 3

in

.1

ft 9

in

.E

iffe

l Tow

er,

Par

is98

4 ft

328

ft

8.4

ft8

in.

Tex

as C

omm

erce

Tow

er,H

oust

on1,

002

ft16

7 ft

9.5

ft 6

in

.11

in

.Jo

hn

Han

cock

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er,B

osto

n79

0 ft

131

ft 8

in

.

10.

5 ft

4 i

n.

8 in

.S

ears

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er,

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icag

o1,

454

ft18

1 ft

9 i

n.

11.

5 ft

6 i

n.

11 in

.B

arn

ett

Tow

er,

Jack

son

vill

e63

1 ft

105

ft 2

in

.



©G

lenc

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cGra

w-H

ill22

2M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice:

Wor

d Pr

oble

ms

Dila

tio

ns

1.EY

ESD

ave’

s op

tom

etri

st u

sed

med

icin

eto

dil

ate

his

eye

s.B

efor

e di

lati

on,h

ispu

pils

had

a d

iam

eter

of

4.1

mil

lim

eter

s.A

fter

dil

atio

n,h

is p

upi

lsh

ad a

dia

met

er o

f 8.

2 m

illi

met

ers.

Wh

at w

as t

he

scal

e fa

ctor

of

the

dila

tion

?2

2.B

IOLO

GY

A m

icro

scop

e in

crea

ses

the

size

of

obje

cts

by a

fac

tor

of 8

.How

larg

e w

ill

a 0.

006

mil

lim

eter

para

mec

ium

app

ear?

0.04

8 m

m

3.PH

OTO

GR

APH

YA

ph

otog

raph

was

enla

rged

to

a w

idth

of

15 i

nch

es.I

f th

esc

ale

fact

or w

as �3 2�,

wh

at w

as t

he

wid

thof

th

e or

igin

al p

hot

ogra

ph?

10 in

.

4.M

OV

IES

Fil

m w

ith

a w

idth

of

35m

illi

met

ers

is p

roje

cted

on

to a

scr

een

wh

ere

the

wid

th i

s 5

met

ers.

Wh

at i

sth

e sc

ale

fact

or o

f th

is e

nla

rgem

ent?

�1,0 700 �

5.PH

OTO

CO

PYIN

GA

10-

inch

lon

g co

py o

fa

2.5-

inch

lon

g fi

gure

nee

ds t

o be

mad

ew

ith

a c

opyi

ng

mac

hin

e.W

hat

is

the

appr

opri

ate

scal

e fa

ctor

?4

6.M

OD

ELS

A s

cale

mod

el o

f a

boat

is

goin

g to

be

mad

e u

sin

g a

scal

e of

� 51 0�.

If t

he

orig

inal

len

gth

of

the

boat

is

20 m

eter

s,w

hat

is

the

len

gth

of

the

mod

el?

0.4

m o

r 40

cm

7.M

OD

ELS

An

arc

hit

ectu

ral

mod

el i

s 30

in

ches

tal

l.If

th

e sc

ale

use

d to

bu

ild

the

mod

el i

s � 11 20�

,wh

at i

s th

e h

eigh

t of

the

actu

al b

uil

din

g?3,

600

in.o

r30

0 ft

8.A

DV

ERTI

SIN

GA

n a

dver

tise

r n

eeds

a4-

inch

pic

ture

of

a 14

-foo

t au

tom

obil

e.W

hat

is

the

scal

e fa

ctor

of

the

redu

ctio

n?

� 41 2�

©G

lenc

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cGra

w-H

ill22

1M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Fin

d t

he

coor

din

ates

of

the

vert

ices

of

tria

ngl

e A

�B�C

�af

ter

tria

ngl

eA

BC

is d

ilat

ed u

sin

g th

e gi

ven

sca

le f

acto

r.T

hen

gra

ph

tri

angl

e A

BC

and

its

dil

atio

n.

1.A

(1,1

),B

(1,3

),C

(3,1

);sc

ale

fact

or 3

2.A

(�2,

�2)

,B(�

1,2)

,C(2

,1);

scal

e fa

ctor

2

A�(

3,3)

,B�(

3,9)

,C�(

9,3)

A�(

�4,

�4)

,B�(

�2,

4),C

�(4,

2)

3.A

(�4,

6),B

(2,6

),C

(0,8

);sc

ale

fact

or �1 2�

4.A

(�3,

�2)

,B(1

,2),

C(2

,�3)

;sca

le f

acto

r 1.

5

A�(

�2,

3),B

�(1,

3),C

�(0,

4)A

�(�

4.5,

�3)

,B�(

1.5,

3),C

�(3,

�4.

5)

Seg

men

t P

�Q�

is a

dil

atio

n o

f se

gmen

t P

Q.F

ind

th

e sc

ale

fact

or o

f th

e d

ilat

ion

and

cla

ssif

y it

as

an e

nla

rgem

ent

or a

red

uct

ion

.

5.6.

�1 2�;re

du

ctio

n2;

2;en

larg

emen

t

7.8.

�2 3�;re

du

ctio

n�3 2�;

enla

rgem

ent

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Lesson X–2

Prac

tice:

Ski

llsD

ilati

on

s

Lesson 4–8

y

xO

A�

C�

B�

B AC

y

xO

A

CB

A�

B�

C�

y

xO

A�

B�

C�

AB

Cy

xO

AC

B

C�

A�

B�

y

xO

P�

Q�

P

Q

y

xO

P�

Q�

P

Q

y

xO

P�

P

QQ

�

y

xO

P�

P

Q

Q�


An

swer

s


©G

lenc

oe/M

cGra

w-H

ill22

4M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

Dila

tio

n a

nd

Are

aA

dil

atio

n o

f a

shap

e cr

eate

s a

new

sh

ape

that

is

sim

ilar

to

the

orig

inal

.Th

e ra

tio

of t

he

new

im

age

to t

he

orig

inal

is

call

ed t

he

scal

e fa

ctor

.

Plo

t an

d d

raw

eac

h s

hap

e.T

hen

per

form

th

e d

ilat

ion

of

each

sh

ape

usi

ng

a sc

ale

fact

or o

f tw

o.A

fter

th

e n

ew i

mag

eh

as b

een

dra

wn

,det

erm

ine

the

area

of

bot

h t

he

orig

inal

shap

e an

d i

ts d

ilat

ion

.S

ee s

tud

ents

’wo

rk.

1.A

(2,1

),B

(7,1

),C

(4,4

)

Are

a of

ori

gin

al _

____

___

7.5

sq.u

nit

s

Are

a of

dil

atio

n _

____

___

30 s

q.u

nit

s

2.ci

rcle

wit

h r

adiu

s (1

,2)

to (

4,2)

Are

a of

ori

gin

al _

____

___

28.2

6 sq

.un

its

Are

a of

dil

atio

n _

____

___

113.

04 s

q.u

nit

s

3.R

(�3,

2),E

(�3,

�2)

,C(4

,�2)

,I(4

,2)

4.S

(�3,

3),Q

(�3,

�3)

,A(3

,�3)

,R(3

,3)

Are

a of

ori

gin

al _

____

___

Are

a of

ori

gin

al _

____

___

28 s

q.u

nit

s36

sq

.un

its

Are

a of

dil

atio

n _

____

___

Are

a of

dil

atio

n _

____

___

112

sq.u

nit

s14

4 sq

.un

its

5.W

hat

gen

eral

sta

tem

ent

can

be

mad

e ab

out

the

area

of

a fi

gure

wh

enco

mpa

red

to i

ts a

rea

afte

r be

ing

dila

ted

by s

cale

fac

tor

2?

Acc

ept

log

ical

res

po

nse

s;th

e ar

ea o

f a

fig

ure

is 4

tim

es g

reat

erw

hen

dila

ted

by

scal

e fa

cto

r 2.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enric

hmen

t

y

xO

©G

lenc

oe/M

cGra

w-H

ill22

3M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 3

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Lesson X–2

Pre-

Act

ivit

yC

om

ple

te t

he

Min

i Lab

at

the

top

of

pag

e 19

4 in

yo

ur

text

bo

ok.

Wri

te y

ou

r an

swer

s b

elo

w.

1.M

ult

iply

eac

h c

oord

inat

e by

2 t

o fi

nd

the

coor

din

ates

of

poin

ts A

�,B

�,an

d C

�.A

�(0,

0),B

�(2,

8),C

�(8,

6)

2.O

n t

he

sam

e co

ordi

nat

e pl

ane,

grap

h p

oin

ts

A�,

B�,

and

C�.

Th

en d

raw

�A

�B�C

�.

3.D

eter

min

e w

het

her

�A

BC

��

A�B

�C�.

Exp

lain

you

r re

ason

ing.

Yes;

corr

esp

on

din

g s

ides

of

the

two

tri

ang

les

are

pro

po

rtio

nal

.

Rea

din

g t

he

Less

on

4.If

you

are

giv

en t

he

coor

din

ates

of

a fi

gure

an

d th

e sc

ale

fact

or o

f a

dila

tion

of

that

fig

ure

,how

can

you

fin

d th

e co

ordi

nat

es o

f th

e n

ewfi

gure

?S

amp

le a

nsw

er:

Mu

ltip

ly e

ach

co

ord

inat

e by

th

esc

ale

fact

or.

5.W

hen

you

gra

ph a

fig

ure

an

d it

s im

age

afte

r a

dila

tion

,how

can

you

chec

k yo

ur

wor

k?S

amp

le a

nsw

er:

Dra

w li

nes

th

rou

gh

th

eo

rig

in a

nd

eac

h o

f th

e ve

rtic

es o

f th

e o

rig

inal

fig

ure

.Th

eve

rtic

es o

f th

e d

ilate

d im

age

sho

uld

lie

on

th

ose

sam

e lin

es.

Hel

pin

g Y

ou

Rem

emb

er6.

Com

plet

e th

e ta

ble

belo

w t

o h

elp

you

rem

embe

r th

e ef

fect

s of

dif

fere

nt

scal

e fa

ctor

s.Read

ing

to L

earn

Mat

hem

atic

sD

ilati

on

s

Lesson 4–8

If t

he

scal

e fa

ctor

is

Th

en t

he

dil

atio

n i

s

betw

een

0 a

nd

1a

red

uct

ion

grea

ter

than

1an

en

larg

emen

t

equ

al t

o 1

the

sam

e si

ze a

s th

e o

rig

inal

fig

ure

y

xO

� A

�

C�

B�

B

A

C


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10. H

C

H

A

I

C

H

D

F

D

7 m

I

B

F

A

F

A

I

D

H

A

F

B

H

A

G

D

H

A

G

B

Chapter 4 Assessment Answer KeyForm 1 Form 2APage 225 Page 226 Page 227

(continued on the next page)


An

swer

s

11.

12.

13.

14.

15.

16.

17.

18.

B:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

B: 12 green beans

F

C

H

D

G

A

H

D

G

D

I

B

H

B

H

A

I

A

8 red marbles

G

A

I

C

F

B

G

D

Chapter 4 Assessment Answer KeyForm 2A (continued) Form 2BPage 228 Page 229 Page 230


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 3 lb, 12 oz

2; enlargement

A��2�14

�, 1�12

��B��1, 2�

12

�� C��14

�, ��12

��D��1�

12

�, �4�

10 ft

72.8 in.

4,312.5 mi

1,868.75 mi

Sample answer:

�52

� � �6x

�; 2.4

Yes; correspondingangles are

congruent and

�63

� � �84

� � �51.15�.

7.2 laps

16.5

27

8; $8 for each hour

y

xO

��12

�;0.02 in./min

0.1 in./min

12 reams for $24.50;12 reams for $24.50 isabout $2.04/ream and5 reams for $15.25 is

$3.05/ream.

59.2 mi/h

�172�

19:21

0

Chapter 4 Assessment Answer KeyForm 2CPage 231 Page 232


An

swer

s

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

G��5�13

�, 1�13

��H��4, 2�

23

��I��6�

23

�, �8�

�12

�; reduction

M��23

�, ��23

��N�(�1, 1), O��

13

�, 1�P��1, �

13

��

31.25 ft

22.4 ft

660 mi

30 mi

Sample answer:

�192� � �

5x

�; 3.75

Yes; correspondingangles are congruent

and �24

� = �12

�.

72 times

12

22.5

�110�; �

110� gal/mi

y

xO

�23

�

35 tickets/min

4 tickets/min

$9.50 for 24 juice boxes; $14.60 for 36 boxes is about

$0.41/box, and $9.50for 24 boxes is about

$0.40/box.

52.5 mi/h

17:22

�171�

�3

Chapter 4 Assessment Answer KeyForm 2DPage 233 Page 234


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 384 g

�12

�; reduction

A��8, �23

��, B�(�5, 16),

C��4, 6�12

��, D�(0, �2)

350 m

120 m

�710�

20�49

� m

Sample answer:

�9600� � �

7x5�; 50 yd

Sample answer:

�156� � �

2x0�; 6.25

$401.25

1.5

1,567.5 mi

495 mi

�4;

�12

�

�1

37.2 cells/day

Between 5 and 6 min;the line segment

between these twotimes is horizontal.

10 ft/min

180 min for $35.95;120 min for $24.95 isabout $0.21/min and180 min for $35.95 is

about $0.20/min.

5:4

Chapter 4 Assessment Answer KeyForm 3Page 235 Page 236


An

swer

s

y

xO

Chapter 4 Assessment Answer Key Page 237, Extended Response Assessment

Scoring Rubric


Level Specific Criteria

4 The student demonstrates a thorough understanding of the mathematicsconcepts and/or procedures embodied in the task. The student hasresponded correctly to the task, used mathematically sound procedures,and provided clear and complete explanations and interpretations. Theresponse may contain minor flaws that do not detract from thedemonstration of a thorough understanding.

3 The student demonstrates an understanding of the mathematics conceptsand/or procedures embodied in the task. The student’s response to thetask is essentially correct with the mathematical procedures used and theexplanations and interpretations provided demonstrating an essential butless than thorough understanding. The response may contain minor errorsthat reflect inattentive execution of the mathematical procedures orindications of some misunderstanding of the underlying mathematicsconcepts and/or procedures.

2 The student has demonstrated only a partial understanding of themathematics concepts and/or procedures embodied in the task. Althoughthe student may have used the correct approach to obtaining a solution ormay have provided a correct solution, the student’s work lacks an essentialunderstanding of the underlying mathematical concepts. The responsecontains errors related to misunderstanding important aspects of the task,misuse of mathematical procedures, or faulty interpretations of results.

1 The student has demonstrated a very limited understanding of themathematics concepts and/or procedures embodied in the task. Thestudent’s response to the task is incomplete and exhibits many flaws.Although the student has addressed some of the conditions of the task, thestudent reached an inadequate conclusion and/or provided reasoning thatwas faulty or incomplete. The response exhibits many errors or may beincomplete.

0 The student has provided a completely incorrect solution oruninterpretable response, or no response at all.


Chapter 4 Assessment Answer Key Page 237, Extended Response Assessment

Sample Answers

1. a. A ratio is a comparison of twonumbers by division.

b. 1 to 2; 1:4; �24�

c. A proportion is an equation thatshows that two ratios are equivalent.

d. �12� � �40

x0� �

42� � �40

x0�

2x � 400 2x � 1,600

x � 200 lbs cement x � 800 lbs gravel

2. a. Two polygons are similar if theircorresponding angles are congruentand their corresponding sides are inproportion.

b. A�B� and E�F�; B�C� and F�G�; C�D� and G�H�;and D�A� and H�E�; You can find theratio of the lengths of one pair ofcorresponding sides where bothlengths are known. Because theratios of the lengths of all thecorresponding sides are equal, youcan use the ratio you found to formproportions to find the lengths of thesides whose lengths are not given—B�C�, E�F�, and G�H�.

c.

5�35� is the same as 5.6.

�58.6� � �2

x�

2(5.6) � 8x

11.2 � 8x

x � 1.4

The man’s shadow is 1.4 feet long.

d. All three involve using proportionsand ratios to find a missingmeasurement.

e. The scale factor would be smallerthan 1 because it is the ratio of thedilated image to the original.

x

8 ft

2 ft

5 ft35

In addition to the scoring rubric found on A28, the following sample answers maybe used as guidance in evaluating extended response assessment items.

An

swer

s

1. false; run

2. false; equal

3. true

4. false; rate

5. true

6. false; similar

7. true

8. true

9. false; scale

10. false; ratio

11. a rate that issimplified so it hasa denominator of 1

12. the parts of similarfigures that “match”

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Quiz (Lessons 4-3 and 4-4)

Page 239

1.

2.

3.

4.

5.

1.

2.

3.

4.

5.

Quiz (Lessons 4-7 and 4-8)

Page 240

1.

2.

3.

4.

5.�14

�; reduction

X��1�12

�, �1�, Y�(0, 0),

Z�(2, 2)

X�(�3, �6), Y�(6, 3),Z�(12, �3)

60 ft

21.6 ft

B

220 mi

35 mi

Sample answer:�8x

� � �2102�; x � 4.8

Sample answer:�1x6� � �

192�; x � 12

3.25

20

24

��12

�

�32

�

week 9 to week 15

�23

� cm/week

�12

� cm/week

2.75 students/computer

$92.50/chair

23 students/teacher

�32

�

�1215�

�130�

�45

�

Chapter 4 Assessment Answer KeyVocabulary Test/Review Quiz (Lessons 4-1 and 4-2) Quiz (Lessons 4-5 and 4-6)

Page 238 Page 239 Page 240


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.�32

�; enlargement

15 ft

90 mi

12.5

��12

�

$ 3.10/lb

�210�

15.7 units

whole, integer,rational

9 or �9

27

256

8�56

�

�1495�

�8

�4

�12

�; �12

� gal of

juice/student

16/mi

5.25 h

� 138 copies/mo

99.5 copies/mo

D

H

C

F

D

Chapter 4 Assessment Answer KeyMid-Chapter Test Cumulative ReviewPage 241 Page 242


An

swer

s

1.

2.

3.

4.

5.

6.

7.

8.

9.

10. 11.

12.

13.

14. a. 41 voters/h; Between 10 A.M.and 12 P.M. an average of 41people voted each hour.

b. Between 2 P.M. and 3 P.M.; therewas no change in the numberof voters during this timeperiod.

c. between 12 P.M. and 2 P.M.

36 ft

�32

�

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

8.8

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

9/8

DCBA

IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

Chapter 4 Assessment Answer KeyStandardized Test PracticePage 243 Page 244


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