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

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Pre-Algebra 7-5 Dilations 7-5 Dilations Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation Slide 2 Pre-Algebra 7-5 Dilations Warm Up Multiply. 1. 4 2. 12 3. 24 4. 36 Pre-Algebra 7-5 Dilations 3 18 10 9 27 30 3434 3434 3434 3434 5. 4 2.56. 12 2.5 Slide 3 Pre-Algebra 7-5 Dilations 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. Slide 4 Pre-Algebra 7-5 Dilations Learn to identify and create dilations of plane figures. Slide 5 Pre-Algebra 7-5 Dilations Vocabulary dilation scale factor center of dilation Slide 6 Pre-Algebra 7-5 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. Slide 7 Pre-Algebra 7-5 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. Slide 8 Pre-Algebra 7-5 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. Slide 9 Pre-Algebra 7-5 Dilations A scale factor between 0 and 1 reduces a figure. A scale factor greater than 1 enlarges it. Helpful Hint Slide 10 Pre-Algebra 7-5 Dilations Tell whether each transformation is a dilation. The transformation is a dilation. The transformation is not a dilation. The figure is distorted. Additional Example 1A & 1B: Identifying Dilations A. B. Slide 11 Pre-Algebra 7-5 Dilations Tell whether each transformation is a dilation. The transformation is a dilation. The transformation is not a dilation. The figure is distorted. Additional Example 1C & 1D: Identifying Dilations C. D. Slide 12 Pre-Algebra 7-5 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. Slide 13 Pre-Algebra 7-5 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 Slide 14 Pre-Algebra 7-5 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. Slide 15 Pre-Algebra 7-5 Dilations Dilate the figure by a scale factor of 1.5 with P as the center of dilation. Additional Example 2: Dilating a Figure Multiply each side by 1.5. Slide 16 Pre-Algebra 7-5 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 FH 1 cm Slide 17 Pre-Algebra 7-5 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 Slide 18 Pre-Algebra 7-5 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(3, 9) A(3, 9 ) A(1, 3) 1313 1313 B(9, 6) B(9, 6 ) B(3, 2) 1313 1313 C(6, 3) C(6, 3 ) C(2, 1) 1313 1313 Multiply the coordinates by to find the vertices of the image. 1313 Slide 19 Pre-Algebra 7-5 Dilations Try This: Example 3A Dilate the figure by a scale factor of 2. What are the vertices of the image? 2 4 2 46 8 10 0 6 8 B C A Slide 20 Pre-Algebra 7-5 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 The vertices of the image are A(4, 4), B(8, 4), and C(4, 8). Slide 21 Pre-Algebra 7-5 Dilations Try This: Example 3A Continued 2 4 2 46 8 10 0 6 8 B C A B C A Slide 22 Pre-Algebra 7-5 Dilations Try This: Example 3B Dilate the figure by a scale factor of 0.5. What are the vertices of the image? 2 4 2 46 8 10 0 6 8 B C A Slide 23 Pre-Algebra 7-5 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 The vertices of the image are A(2, 2.5), B(4, 2.5), and C(2, 4.5). Slide 24 Pre-Algebra 7-5 Dilations Try This: Example 3B Continued 2 4 2 46 8 10 0 6 8 B C A B C A Slide 25 Pre-Algebra 7-5 Dilations 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) 246 -2 -4 -6 P A B C 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)