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**7-5 Dilations Warm Up Problem of the Day Lesson Presentation**

Pre-Algebra

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**7-5 Dilations Warm Up Multiply. 1. 4 2. 12 3. 24 4. –36 3 9 18**

Pre-Algebra 7-5 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 scale factor center of 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.

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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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**A scale factor describes how much a figure is enlarged or reduced**

A scale factor describes how much a figure is enlarged or reduced. A scale factor can be expressed as a decimal, fraction, or percent. A 10% increase is a scale factor of 1.1, and a 10% decrease is a scale factor of 0.9.

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**A scale factor between 0 and 1 reduces a figure**

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 1A & 1B: Identifying Dilations**

Tell whether each transformation is a dilation. A. B. The transformation is not a dilation. The figure is distorted. The transformation is a dilation.

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**Additional Example 1C & 1D: 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.**

Try This: Example 1A & 1B Tell whether each transformation is a dilation. B A C A. A B C 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.**

Try This: Example 1C & 1D 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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**Every dilation has a fixed point that is the center of dilation**

Every dilation has a fixed point that is the center of dilation. To find the center of dilation, draw a line that connects each pair of corresponding vertices. The lines intersect at one point. This point is the center of dilation.

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**Additional Example 2: Dilating a Figure**

Dilate the figure by a scale factor of 1.5 with P as the center of dilation. Multiply each side by 1.5.

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Try This: Example 2 Dilate the figure by a scale factor of 0.5 with G as the center of dilation. G F H 2 cm F’ H’ 1 cm G 2 cm 2 cm F H 2 cm Multiply each side by 0.5.

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

Dilate the figure in Example 3A on page 363 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**

Dilate the figure in Example 3B by a scale factor of . What are the vertices of the image? 1 3 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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Try This: 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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**Try This: 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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**Try This: Example 3A Continued**

10 B’ C’ A’ 8 6 C 4 2 A B 2 4 6 8 10

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Try This: 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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**Try This: 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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**Try This: Example 3B Continued**

10 C 8 6 B’ C’ A’ A B 4 2 2 4 6 8 10

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**1. Tell whether the transformation is a dilation. **

Lesson Quiz 1. Tell whether the transformation is a dilation. A(0, 4) B(5,5) C(3,3) A’(0, 8) B’(10, 10) C’(6, 6) 2 4 6 2. Dilate the figure by a scale factor of 1.5 with P as the center of dilation. P A B C -2 3. Dilate the figure by a scale factor of 2 with the origin as the center of dilation. What are the coordinates of the image? A(2,4) B(5,6) C(6,1) -4 -6

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Warm Up (4, –6) (12, 27) (–6, 2) 1. Subtract 3 from the x-coordinate and 2 from the y-coordinate in (7, –4). 2. Multiply each coordinate by 3 in (4, 9).

Warm Up (4, –6) (12, 27) (–6, 2) 1. Subtract 3 from the x-coordinate and 2 from the y-coordinate in (7, –4). 2. Multiply each coordinate by 3 in (4, 9).

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