7.6 ESSENTIAL QUESTION How do you identify and draw dilations?

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Presentation transcript:

7.6 ESSENTIAL QUESTION How do you identify and draw dilations?

VOCABULARY

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.

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).

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

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

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

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

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

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

Homework Worksheet 7.6A