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

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

Course 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.

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

Course Dilations Vocabulary dilation center of dilation

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. 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.

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.

Course 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 1: Identifying Dilations A. B.

Course 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 1: Identifying Dilations C. D.

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. Check It Out: Example 1 B.

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. Check It Out: Example 1 A'A' B'B' C'C' A B C D. A'A' B'B' C'C' A B C

Course 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.

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. Check It Out: Example 2 G FH 2 cm F’H’ 1 cm

Course Dilations 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

Course Dilations 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(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’

Course Dilations Additional Example 3B: Using the Origin as the Center of Dilation Dilate the figure below 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

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

Course Dilations Check It Out: 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).

Course Dilations Check It Out: Example 3A Continued B’ C’ A’ B C A

Course Dilations Check It Out: Example 3B Dilate the figure by a scale factor of 0.5. What are the vertices of the image? B C A

Course Dilations Check It Out: 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).

Course Dilations Check It Out: Example 3B Continued B C A B’ C’ A’

Course 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) 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