Geo-Activity. 1 Draw a triangle. Label it TPQR. Choose a point C outside the triangle. P on CP&*(such that CP 2 p CP. Locate Q and R the same way.

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1 age 1 of 7. Dilations Goal Identify and draw dilations. Key Words dilation reduction enlargement Geo-Activity Drawing a Dilation 1 Draw a triangle. Label it TQ. hoose a point outside the triangle. 2 Use a straightedge to draw lines from through, Q, and. 3 Measure &* and locate a point on &*(such that 2 p. Locate Q and the same way. onnect the points, Q, and to form T Q. 5 alculate the ratios, Q Q, and Q Q. Then show that TQ is similar to T Q. What is the scale factor of T Q to TQ? ow does it compare to the ratio? Student elp LOOK BAK To review other types of transformations, see pp. 152 and 22. A dilation is a transformation with center and scale factor k that maps each point to an image point so that lies on &*( and kp. As you saw in the Geo-Activity above, a dilation maps a figure onto a similar figure, called the image. center of dilation k p point image 7. Dilations 393

2 age 2 of Types of Dilations If the image is smaller than the original figure, then the dilation is a reduction. If the image is larger than the original figure, then the dilation is an enlargement. Visualize It! original image For transformations in this book, the original figure is blue and the image is red. EXAMLE Tell whether the dilation is a reduction or an enlargement. a. b. X Solution 1 Identify Dilations a. The dilation is an enlargement because the image (T Q ) is larger than the original figure (T Q). b. The dilation is a reduction because the image (T X Y Z ) is smaller than the original figure (T XYZ ). X Z Z Y Y Student elp STUDY TI If you know the scale factor k of a dilation, you can tell the type of dilation. If k < 1, then the dilation is a reduction. If k > 1, then the dilation is an enlargement. Scale Factor The scale factor of a dilation is the ratio of to. This is also equal to the scale factor of T Q to T Q. scale factor k Q Q EXAMLE 2 Find Scale Factors Find the scale factor of the dilation. a. b Solution Find the ratio of to. a. scale factor 2 3 b. scale factor hapter 7 Similarity

3 age 3 of Identify Dilations and Find Scale Factors Tell whether the dilation is a reduction or an enlargement. Then find the scale factor of the dilation Student elp STUDY TI ecall that the scale factor of the dilation equals the ratio of the corresponding sides of the figures. EXAMLE T Q is the image of T Q after a reduction. Find the value of x. Solution Q Q 1 x Write a proportion. p x p ross product property x 3 Dilations and Similar Figures Substitute for, for, for Q, and x for Q. Multiply. x 10.5 Divide each side by. x Dilations and Similar Figures The red figure is the image of the blue figure after a dilation. Find the value of the variable.. 5. m 2 20 n 3 7. Dilations 395

4 age of 7. Exercises Guided ractice Vocabulary heck 1. omplete: In a dilation, every image is? to the original figure. Skill heck 2. Error Analysis Katie found the scale factor of the dilation shown to be 1. What did Katie do wrong? Is the dilation shown a reduction or an enlargement? ow do you know? 2 1 scale factor 2 Tell whether the dilation is a reduction or an enlargement.. 5. S S Y X Z Y X Z ractice and Applications Extra ractice See p.. Identifying Dilations Tell whether the dilation is a reduction or an enlargement. Then find its scale factor omework elp Example 1: Exs. 9, 11 Example 2: Exs. 9, 15 Example 3: Exs. 11, Visualize It! Sketch quadrilateral EFG. Then sketch a dilation of EFG with center and scale factor hapter 7 Similarity

5 age 5 of Dilations and Similar Figures The red figure is the image of the blue figure after a dilation. Tell whether the dilation is a reduction or an enlargement. Then find the value of the variable x n y m 2 IStudent elp I L A S S Z O N E. O M OMEWOK EL Extra help with problem solving in Exs is at classzone.com Flashlight Image In Exercises 15 and 1, use the following information and the diagram below. The flashlight in the photograph below has a removable clear cap with a picture of a bug on it. When the flashlight is on, the bug is projected onto a wall. This situation models a dilation. 15. What is the scale factor of the dilation? 1. Write and solve a proportion to find the height of the bug projected onto the wall. h 2 cm 2.5 cm 10 cm Standardized Test ractice 17. Multiple hoice The length of a side of K L M is what percent of the length of the corresponding side of KLM? A 3% B 12% % D 300% K L M 2 M K 10 L 7. Dilations 397

6 age of Mixed eview Finding Angle Measures Find the measure of a1. (Lesson.2) 1. A 19. F B G L K Solving roportions Solve the proportion. (Lesson 7.1) 21. d x 1 2 t 3 12 Algebra Skills Evaluating Expressions Evaluate the expression when x 3. (Skills eview, p. 70) 2. x x 9 2. (x 2)(x 5) x 3 x 29. x 2 3x 1 Quiz 2 Determine whether the triangles are similar. If they are similar, write a similarity statement. (Lesson 7.) 1. A 2. 7 F B L 10 K G Find the value of the variable. (Lesson 7.5) 3. A. F 5. x 10 D E y K S z 22 T B 3 G Tell whether the dilation is a reduction or an enlargement. Then find its scale factor. (Lesson 7.) hapter 7 Similarity