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5-6 Dilations Course 3 Warm Up Problem of the Day Lesson Presentation

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**5-6 Dilations Warm Up Multiply. 1. 4 2. 12 3. 24 4. –36 3 9 18**

Course 3 5-6 Dilations Warm Up Multiply. 1. 4 3. 24 –36 3 4 3 4 3 9 3 4 3 4 18 –27 5. 4 2.5 10 30

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Problem of the Day Every day, a plant grows to three times its size. Every night, it shrinks to half its size. After three days and nights, it is 6.75 in. tall. How tall was the plant at the start? 2 in.

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**Learn to identify and create dilations of plane figures.**

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Vocabulary dilation

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**Your pupils are the black areas in the center of your eyes**

Your pupils are the black areas in the center of your eyes. When you go to the eye doctor, the doctor may dilate your pupils, which makes them larger. Translations, reflections, and rotations are transformations that do not change the size or shape of a figure. A dilation is a transformation that changes the size, but not the shape, of a figure. A dilation can enlarge or reduce a figure.

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**Additional Example 1: Identifying Dilations**

Tell whether each transformation is a dilation. D. C. The transformation is not a dilation. The figure is distorted. The transformation is a dilation.

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**Tell whether each transformation is a dilation.**

Check It Out: Example 1 Tell whether each transformation is a dilation. B A C A' B' C' A. A B C B. A' B' C' The transformation is a dilation. The transformation is not a dilation. The figure is distorted.

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**Tell whether each transformation is a dilation.**

Check It Out: Example 1 Tell whether each transformation is a dilation. D. A' B' C' A B C C. A' B' C' A B C The transformation is not a dilation. The figure is distorted. The transformation is a dilation.

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**Additional Example 2: Dilating a Figure**

Dilate the figure by a scale factor of 1.5 Multiply each side by 1.5.

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Check It Out: Example 2 Dilate the figure by a scale factor of 0.5 with G as the center of dilation. G 2 cm 2 cm F H 2 cm Multiply each side by 0.5.

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**Insert Lesson Title Here**

Course 3 5-6 Dilations Insert Lesson Title Here A scale factor between 0 and 1 reduces a figure. A scale factor greater than 1 enlarges it. Helpful Hint

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**Additional Example 3A: Using the Origin as the Center of Dilation**

Dilate the figure below by a scale factor of 2. What are the vertices of the image? Multiply the coordinates by 2 to find the vertices of the image. A’B’C’ ABC A(4, 8) A’(4 2, 8 2) A’(8, 16) B(3, 2) B’(3 2, 2 2) B’(6, 4) C(5, 2) C’(5 2, 2 2) C’(10, 4) The vertices of the image are A’(8, 16), B’(6, 4), and C’(10, 4).

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**Additional Example 3B: Using the Origin as the Center of Dilation**

1 3 Dilate the figure below by a scale factor of . What are the vertices of the image? Multiply the coordinates by to find the vertices of the image. 1 3 A’B’C’ ABC A(3, 9) A’(3 , 9 ) A’(1, 3) 1 3 B(9, 6) B’(9 , 6 ) B’(3, 2) 1 3 C(6, 3) C’(6 , 3 ) C’(2, 1) 1 3 The vertices of the image are A’(1, 3), B’(3, 2), and C’(2, 1).

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Check It Out: Example 3A Dilate the figure by a scale factor of 2. What are the vertices of the image? 10 8 6 C 4 2 A B 2 4 6 8 10

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**Check It Out: Example 3A Continued**

A’B’C’ ABC A(2, 2) A’(2 2, 2 2) A’(4, 4) B(4, 2) B’(4 2, 2 2) B’(8, 4) C(2, 4) C’(2 2, 4 2) C’(4, 8) The vertices of the image are A’(4, 4), B’(8, 4), and C’(4, 8).

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**Check It Out: Example 3A Continued**

10 B’ C’ A’ 8 6 C 4 2 A B 2 4 6 8 10

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Check It Out: Example 3B Dilate the figure by a scale factor of What are the vertices of the image? 10 C 8 6 A B 4 2 2 4 6 8 10

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**Check It Out: Example 3B Continued**

A’B’C’ ABC A(4, 5) A’(4 0.5, 5 0.5) A’(2, 2.5) B(8, 5) B’(8 0.5, 5 0.5) B’(4, 2.5) C(4, 9) C’(4 0.5, 9 0.5) C’(2, 4.5) The vertices of the image are A’(2, 2.5), B’(4, 2.5), and C’(2, 4.5).

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**Check It Out: Example 3B Continued**

10 C 8 6 B’ C’ A’ A B 4 2 2 4 6 8 10

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