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![Page 1: The Distance Formula - coalg.weebly.com€¦ · The Distance Formula . Example Find the distance between (1, 4) and (-2, 3). Round to the nearest hundredths. D = 3.16 2 2 1 2 D 2](https://reader034.vdocument.in/reader034/viewer/2022042502/5f7c88c6a824961f5f6ea63a/html5/thumbnails/1.jpg)
11, yx 22 , yx
2 2
2 1 2 1( ) ( )D x x y y
The Distance Formula
![Page 2: The Distance Formula - coalg.weebly.com€¦ · The Distance Formula . Example Find the distance between (1, 4) and (-2, 3). Round to the nearest hundredths. D = 3.16 2 2 1 2 D 2](https://reader034.vdocument.in/reader034/viewer/2022042502/5f7c88c6a824961f5f6ea63a/html5/thumbnails/2.jpg)
Example Find the distance between (1, 4) and (-2, 3). Round to the nearest hundredths.
D = 3.16
2
12
2
12 )()(D yyxx
22 )43()12(D
22 )1()3(D
19D
10D
![Page 3: The Distance Formula - coalg.weebly.com€¦ · The Distance Formula . Example Find the distance between (1, 4) and (-2, 3). Round to the nearest hundredths. D = 3.16 2 2 1 2 D 2](https://reader034.vdocument.in/reader034/viewer/2022042502/5f7c88c6a824961f5f6ea63a/html5/thumbnails/3.jpg)
Example
Find the distance between the points, (10, 5) and (40, 45). Round to the nearest hundredths.
2
12
2
12 )()(D yyxx
22 )545()1040(D
22 )40()30(D
1600900D
2500D
D = 50
![Page 4: The Distance Formula - coalg.weebly.com€¦ · The Distance Formula . Example Find the distance between (1, 4) and (-2, 3). Round to the nearest hundredths. D = 3.16 2 2 1 2 D 2](https://reader034.vdocument.in/reader034/viewer/2022042502/5f7c88c6a824961f5f6ea63a/html5/thumbnails/4.jpg)
3. Find the distance between the points.
Round to the nearest tenths.
( ) ( )4 1 2 02 2
9 4
13
212
2
12 yyxx
![Page 5: The Distance Formula - coalg.weebly.com€¦ · The Distance Formula . Example Find the distance between (1, 4) and (-2, 3). Round to the nearest hundredths. D = 3.16 2 2 1 2 D 2](https://reader034.vdocument.in/reader034/viewer/2022042502/5f7c88c6a824961f5f6ea63a/html5/thumbnails/5.jpg)
4. Find the distance between the points.
Round to the nearest tenths.
212
2
12 yyxx
![Page 6: The Distance Formula - coalg.weebly.com€¦ · The Distance Formula . Example Find the distance between (1, 4) and (-2, 3). Round to the nearest hundredths. D = 3.16 2 2 1 2 D 2](https://reader034.vdocument.in/reader034/viewer/2022042502/5f7c88c6a824961f5f6ea63a/html5/thumbnails/6.jpg)
Pythagorean Theorem
2 2 2leg leg hyp
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Pythagorean Theorem Word Problems
• A square has a diagonal with length of
20 cm. What is the measure of each
side? Round to the nearest tenths.
x = 14.1 cm
![Page 8: The Distance Formula - coalg.weebly.com€¦ · The Distance Formula . Example Find the distance between (1, 4) and (-2, 3). Round to the nearest hundredths. D = 3.16 2 2 1 2 D 2](https://reader034.vdocument.in/reader034/viewer/2022042502/5f7c88c6a824961f5f6ea63a/html5/thumbnails/8.jpg)
Pythagorean Theorem Word Problems
• A 25 foot ladder is leaning against a
building. The foot of the ladder is 15
feet from the base of the building.
How high is the top of the ladder
along the building? Round to the
nearest tenths.
x = 20 ft
![Page 9: The Distance Formula - coalg.weebly.com€¦ · The Distance Formula . Example Find the distance between (1, 4) and (-2, 3). Round to the nearest hundredths. D = 3.16 2 2 1 2 D 2](https://reader034.vdocument.in/reader034/viewer/2022042502/5f7c88c6a824961f5f6ea63a/html5/thumbnails/9.jpg)
Pythagorean Theorem Word Problems
• Ashley travels 42 miles east, then 19
miles south. How far is Ashley from
the starting point? Round to the
nearest tenths.
x = 46.1 miles
![Page 10: The Distance Formula - coalg.weebly.com€¦ · The Distance Formula . Example Find the distance between (1, 4) and (-2, 3). Round to the nearest hundredths. D = 3.16 2 2 1 2 D 2](https://reader034.vdocument.in/reader034/viewer/2022042502/5f7c88c6a824961f5f6ea63a/html5/thumbnails/10.jpg)
Pythagorean Theorem Word Problems
• What is the length of the altitude of an
equilateral triangle if a side is 12 cm?
Round to the nearest tenths.
x = 10.4 cm
![Page 11: The Distance Formula - coalg.weebly.com€¦ · The Distance Formula . Example Find the distance between (1, 4) and (-2, 3). Round to the nearest hundredths. D = 3.16 2 2 1 2 D 2](https://reader034.vdocument.in/reader034/viewer/2022042502/5f7c88c6a824961f5f6ea63a/html5/thumbnails/11.jpg)
Classwork Round to the nearest tenths.
Worksheet
![Page 12: The Distance Formula - coalg.weebly.com€¦ · The Distance Formula . Example Find the distance between (1, 4) and (-2, 3). Round to the nearest hundredths. D = 3.16 2 2 1 2 D 2](https://reader034.vdocument.in/reader034/viewer/2022042502/5f7c88c6a824961f5f6ea63a/html5/thumbnails/12.jpg)
Classwork / Homework Quadrilaterals Task
![Page 13: The Distance Formula - coalg.weebly.com€¦ · The Distance Formula . Example Find the distance between (1, 4) and (-2, 3). Round to the nearest hundredths. D = 3.16 2 2 1 2 D 2](https://reader034.vdocument.in/reader034/viewer/2022042502/5f7c88c6a824961f5f6ea63a/html5/thumbnails/13.jpg)
Conclusions Parallel
• Same slope
means sides are
parallel
• Opposite
reciprocal slopes
mean
perpendicular
segments (90)
Distance
• Same distance
means segments
are congruent