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Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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Warm Up Solve. 1. 2. x = 12 x = 2.5 2

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Problem of the Day Missy ate one-fourth of a fruit salad and Kim ate one-eighth of the fruit salad. What fraction of the fruit salad remains? 3

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**Sunshine State Standards**

MA.7.G.4.2 Predict the results of transformations and draw transformed figures, with and without the coordinate plane.

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A dilation is a transformation that changes the size, but not the shape, of a figure. After a dilation, the image of a figure is similar to the preimage.

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**Additional Example 1A: Identifying Dilations**

Tell whether each transformation is a dilation. The figures are not similar, so the transformation is not a dilation.

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**Additional Example 1B: Identifying Dilations**

Tell whether each transformation is a dilation. The figures are similar, so the transformation Is a dilation.

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

Check It Out: Example 1A Tell whether each transformation is a dilation. A B A’ B’ 3 cm 6 cm C’ D’ 5 cm D C 10 cm The figures are similar, so the transformation is a dilation.

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

Check It Out: Example 1B Tell whether each transformation is a dilation. Y X’ 13 yd 6 yd 6 yd 5 yd X z z’ 6 yd Y’ 12 yd The figures are not similar, so the transformation is not a dilation. 9

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**Similar figures have the same shape but not necessarily the same size.**

Remember!

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**Additional Example 2: Using Dilation to Enlarge a Figure**

Draw the vertices of the image of ∆ABC after a dilation by a scale factor of 2. What are the vertices of the image? Write the coordinates of the vertices of ABC. Then multiply the coordinates by 2 to find the coordinates of the vertices of A'B'C'.

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**Additional Example 2 Continued**

A’B’C’ ABC A(0, 0) A’(0 2, 0 2) A’(0, 0) B(1, 2) B’(1 2, 2 2) B’(2, 4) C(3, 1) C’(3 2, 1 2) C’(6, 2) The vertices of the image are A’(0, 0), B’(2, 4), and C’(6, 2).

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**Additional Example 2 Continued**

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Check It Out: Example 2A Find the vertices of the image of each figure after a dilation by the given scale factor. Then draw the image. Scale factor 3 R' (0, 12), S' (12, 6), T' (6, 3)

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Check It Out: Example 2B Find the vertices of the image of each figure after a dilation by the given scale factor. Then draw the image. Scale factor 2 A' (4, 10), B' (10, 10),C' (10, 4), D' (4, 4)

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**Additional Example 3: Using a Dilation to Reduce a Figure**

Draw the image of ∆DEF after a dilation by a scale factor of Then draw the image. 1 3 Write the coordinates of the vertices of DEF. The multiply the coordinates by 1/3 to find the coordinates of the vertices of D‘E‘F'. D’E’F’ DEF D(3, 3) D’(3 , 3 ) D’(1, 1) 1 3 E(6, 6) E’(6 , 6 ) E’(2, 2) 1 3 F(9, 3) F’(9 , 3 ) F’(3, 1) 1 3 The vertices of the image are D’(1, 1), E’(2, 2), and F’(3, 1).

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Check It Out: Example 3A Find the vertices of the image of each figure after a dilation by the given scale factor. Then draw the image. 1 3 Scale factor A' (1, 2), B' (1, 4),C' (3, 4),D' (3, 2)

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Check It Out: Example 3B Find the vertices of the image of each figure after a dilation by the given scale factor. Then draw the image. 1 4 Scale factor D' (1, 2), E' (2, 3), F' (3, 2)

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**Lesson Quiz for Student Response Systems**

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 19

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

Lesson Quiz Tell whether the transformation is a dilation. 1. yes 2. Find the vertices of the image of ∆ABC after a dilation of a scale factor of 2. Then draw the image. A'(2, 4), B'(4, 6), C'(8, 0) 20

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**Lesson Quiz for Student Response Systems**

1. Tell whether the transformation is a dilation. A. dilation B. not a dilation 21

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**Lesson Quiz for Student Response Systems**

2. Tell whether the transformation is a dilation. A. dilation B. not a dilation 22

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