1. 7.6
ESSENTIAL QUESTION
How do you identify and draw dilations?

2. VOCABULARY

3. A dilation is called a reduction if the image is smaller than the original figure.
A dilation is called an enlargement if the image is larger than the original figure.

4. Tell whether the dilation is a reduction or an enlargement.
Example 1
Identify Dilations
Tell whether the dilation is a reduction or an enlargement. a. b.
SOLUTION a.
The dilation is an enlargement because the image (P'Q'R') is larger than the original figure (PQR). b.
The dilation is a reduction because the image (X'Y'Z' ) is smaller than the original figure (XYZ).

6. Find the scale factor of the dilation.
Example 2
Find Scale Factors
Find the scale factor of the dilation. a. b.
SOLUTION
Find the ratio of CP' to CP. a.
scale factor = CP
CP' = 3 2 b.
scale factor = CP
CP' = 3 6
= 2

7. Checkpoint
Identify Dilations and Find Scale Factors
Tell whether the dilation is a reduction or an enlargement. Then find the scale factor of the dilation. 1.
enlargement; 2
ANSWER 2.
ANSWER
reduction; 3 1 3.
ANSWER
reduction; 7 3

8. P'Q'R' is the image of PQR after a reduction. Find the value of x.
Example 3
Dilations and Similar Figures
P'Q'R' is the image of PQR
after a reduction.
Find the value of x.
SOLUTION
Write a proportion. CP
CP' = QR
Q'R' 14 8 = x 6
Substitute 8 for CP', 14 for CP, 6 for Q' R', and x for QR.
8 · x = 14 · 6
Cross product property
8x = 84
Multiply.
x = 10.5
Divide each side by 8. 8

9. Checkpoint
Dilations and Similar Figures
The red figure is the image of the blue figure after a dilation. Find the value of the variable. 4.
ANSWER 5 5.
ANSWER 2 9

10. Solve the proportion. 1. 9 4 = 45 x
ANSWER
x = 20 2. n 49 = 12 7
ANSWER
n = 84
Find the value of the variable. 3.
ANSWER
x = 32 4.
ANSWER
y = 11

11. 5.
Given the diagram, determine whether QS is parallel to PT.
ANSWER 7 56 = 1 8
and 6 48
Because
, QS || PT.

12. Homework
Worksheet 7.6A