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7-5 Dilations Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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Warm Up Multiply 2. 12 4. –36 Course Dilations – 2.5

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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. Course Dilations

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Learn to identify and create dilations of plane figures. Course Dilations

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Vocabulary dilation scale factor center of dilation Insert Lesson Title Here Course Dilations

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

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Tell whether each transformation is a dilation. Insert Lesson Title Here Course Dilations The transformation is a dilation. The transformation is not a dilation. The figure is distorted. Additional Example 1A & 1B: Identifying Dilations A. B.

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Tell whether each transformation is a dilation. Insert Lesson Title Here Course Dilations The transformation is a dilation. The transformation is not a dilation. The figure is distorted. Additional Example 1C & 1D: Identifying Dilations C. D.

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Course Dilations Tell whether each transformation is a dilation. A'A' B' B'C'C' A BC A. B A C A'A' B' B'C'C' The transformation is a dilation. The transformation is not a dilation. The figure is distorted. Try This: Example 1A & 1B B.

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Course Dilations Tell whether each transformation is a dilation. C. The transformation is a dilation. The transformation is not a dilation. The figure is distorted. Try This: Example 1C & 1D A'A' B'B' C'C' A B C D. A'A' B'B' C'C' A B C

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Insert Lesson Title Here Course Dilations 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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Dilate the figure by a scale factor of 1.5 with P as the center of dilation. Insert Lesson Title Here Course Dilations Additional Example 2: Dilating a Figure Multiply each side by 1.5.

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

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Insert Lesson Title Here Course Dilations 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(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). ABC A’B’C’

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Insert Lesson Title Here Course Dilations 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? 1313 The vertices of the image are A’(1, 3), B’(3, 2), and C’(2, 1). ABC A’B’C’ A(3, 9) A’(3 , 9 ) A’(1, 3) B(9, 6) B’(9 , 6 ) B’(3, 2) C(6, 3) C’(6 , 3 ) C’(2, 1) Multiply the coordinates by to find the vertices of the image. 1313

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Insert Lesson Title Here Course Dilations Try This: Example 3A Dilate the figure by a scale factor of 2. What are the vertices of the image? B C A

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Insert Lesson Title Here Course Dilations Try This: Example 3A Continued 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) ABC A’B’C’ The vertices of the image are A’(4, 4), B’(8, 4), and C’(4, 8).

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Insert Lesson Title Here Course Dilations Try This: Example 3A Continued B’ C’ A’ B C A

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Insert Lesson Title Here Course Dilations Try This: Example 3B Dilate the figure by a scale factor of 0.5. What are the vertices of the image? B C A

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Insert Lesson Title Here Course Dilations Try This: Example 3B Continued 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) ABC A’B’C’ The vertices of the image are A’(2, 2.5), B’(4, 2.5), and C’(2, 4.5).

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Insert Lesson Title Here Course Dilations Try This: Example 3B Continued B C A B’ C’ A’

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Lesson Quiz Insert Lesson Title Here Course Dilations 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) P A B C C’C’ B’B’A’A’ 2. Dilate the figure by a scale factor of 1.5 with P as the center of dilation. 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) A’(4,8) B’(10,12) C’(12,2) yes

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