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Understanding Dilations: Identify, Draw, and Determine Scale Factors

Learn how to identify and draw dilations, differentiate between enlargements and reductions, and find scale factors with examples and solutions.

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Understanding Dilations: Identify, Draw, and Determine Scale Factors

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  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. 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). Example 1 Identify Dilations Tell whether the dilation is a reduction or an enlargement.

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

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

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

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

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

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

  11. Homework • Worksheet 7.6A

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