web view3/3/2015 · if the distance of a line segment is . 120 , what is the exact...

Cornell Notes

Learning Target (LT):I can calculate the distance between two points.(Standard G.GPE.4)

Name:Class: Coord. AlgebraPeriod:Date: March 13, 2015

Questions Notes

Refresher: Simplifying Radical Expressions

The product of two radicals is the product of the individual radicals

the √❑ of a number is the same as the number to the power of ½

When an answer cannot be negative (like distance), we have:

When the denominator is not a perfect square, we should rationalize the denominator.

When two numbers have different radical values, they cannot be combined.

2√x+3√ x=5√x

2√x+3√ y=2√ x+3√ y

When simplifying radical expressions, factor out the perfect squares and leave the other factors in the radicand.

√16 x = √16 ∙√x= √42∙√ x= 4 √x

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Cornell Notes



Questions

Notes

Warm-up:

1. √51∙√3∙√17=¿

2. If the distance of a line segment is √120 , what is the exact equivalent value in simplified expression?

3. If the distance of a line segment is √120 , what is distance rounded to the nearest one-hundredth?

4. 2√3+5√12=¿

5. Simplify √16( y−2)2 =

Yesterday, we re-visited the PYTHAGOREAN THEOREM and applied it to distance in a coordinate plane. Today, we advance that concept AND start to see where we can use the distance formula to calculate parts of a geometric figure, like a triangle or quadrilateral.

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Cornell Notes



Questions

Notes

Example 1: Find the distance of AB.

1. Find the coordinatesA = B =

2. Designate (x1 y1) and (x2 y2) Let A be (x1 y1) Let B be (x2 y2)

3. Apply the distance formula

4. Simplify the radical expression

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Cornell Notes



Questions

Notes

Example 2: Parallelogram DEFG is shown on at coordinate grid. What is the perimeter of parallelogram DEFG?

Step 1: Determine what lengths to find.

Step 2: Identify the coordinates.

Step 3: Calculate the required distances.

Step 4: ANSWER THE QUESTION.

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Cornell Notes



Questions

Notes

Example 3: Right triangle QRS is shown on the coordinate plane. Find the area of QRS.


Step 2: Identify the coordinates



Key Learnings:1. 2. 3. 4.

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Cornell Notes


Name: TEACHER NOTESClass: Coord. AlgebraPeriod:Date: March 13, 2015

Questions Notes

Refresher: Simplifying Radical Expressions

The product of two radicals is the product of the individual radicals

the √❑ of a number is the same as the number to the power of ½

When an answer cannot be negative (like distance), we have:

When the denominator is not a perfect square, we should rationalize the denominator.

When two numbers have different radical values, they cannot be combined.

2√x+3√ x=5√x

2√x+3√ y=2√ x+3√ y

When simplifying radical expressions, factor out the perfect squares and leave the other factors in the radicand.

√16 x = √16 ∙√x= √42∙√ x= 4 √x

8

Cornell Notes



Questions

Notes

Warm-up:

1. √51∙√3∙√17=¿ √3 ∙17 ∙3 ∙17 = 51

2. If the distance of a line segment is √120 , what is the exact equivalent value in simplified expression? √22 ∙30 = 2√30

3. If the distance of a line segment is √120 , what is distance rounded to the nearest one-hundredth? 1200.5 = 10.95445 = 10.95Distance can only be positive.

4. 2√3+5√12=2√3+5√4∗3=2√3+10√3=12√3

5. Simplify √16( y−2)2 = √16 x √( y−2)2 = 4 ( y – 2)Technically, the signs can be positive or negative.

Yesterday, we re-visited the PYTHAGOREAN THEOREM and applied it to distance in a coordinate plane. Today, we advance that concept AND start to see where we can use the distance formula to calculate parts of a geometric figure, like a triangle or quadrilateral.

9

Cornell Notes



Questions

Notes

Example 1: Find the distance of AB.

1. Find the coordinatesA = (-4,3).B = (4-1)

2. Designate (x1 y1) and (x2 y2) Let A be (x1 y1)Let B be (x2 y2)

3. Apply the distance formula

4. Simplify the radical expression√80=√16 ∙5=4√5 unitsThe distance is positive.

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Cornell Notes



Questions

Notes

Example 2: Parallelogram DEFG is shown on at coordinate grid. What is the perimeter of parallelogram DEFG?


Recall that opposite sides of a parallelogram are congruent. So, we only need to find the lengths of two adjacent sides. So, we need to find the lengths of DE and EF.

Step 2: Identify the coordinates.

D = (-6,1) E = (-3, 5) and F = (5,5).


For DE, we use of distance formula: DE = √(−3−(−6))2+(5−1)2=√(3)2+(4)2=√9+16=√25=5units .

For EF, we see that the line is horizontal, so we don’t need to use the distance formula. We can simply calculate the distance in the change in “x”.

EF = |−3−5|=|−8|=8units .


We were asked to calculate the perimeter. P = DE + EF + FG + GD.Recall that in our parallelogram, DE = FG = 5 units and EF = GD = 8 units.So, perimeter = 5 + 8 + 5 + 8 = 26 units.

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It’s easier to list the points that go back and forth from the graph and

mess up our calculations

If we don’t know our GEOMETRIC SHAPES, then the calculations become a lot longer. Here, the parallelogram has opposite congruent side, meaning

we don’t have to calculate all four sides SEPARATELY.

Cornell Notes



Questions

Notes

Example 3: Right triangle QRS is shown on the coordinate plane. Find the area of QRS.


QRS is a right triangle with the right angle at Q. With a right , the legs form the base and height, so we have to find QR and QS ONLY.

Step 2: Identify the coordinates

Q = (5,2) R = (1,6) and S = (8,5).


Using the distance formula: QR = √(1−5)2+(6−2)2=√(−4 )2+(4 )2=√16+16=√32=4√2 . QS = √(8−5)2+(5−2)2=√(3)2+(3)2=√9+9=√18=3√2 .


Area = ½ (base) (height) = ½ (QR) (QS) = ½ (4 √2) (3√2) = 12 square units.

Thus, the area of QRS is 12 units2

Key Learnings:1. Master the DISTANCE FORMULA2. Know the structure of the geometric shape to save time and reduce the risk

of error.3. Know the rules for simplifying radical expressions.

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Again, KNOWING OUR GEOMETRIC FIGURE saves use time and reduces the

risk of calculation errors

web view3/3/2015 · if the distance of a line segment is . 120 , what is the exact...

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