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Understanding Dilations: Enlargement & Reduction in Plane Figures

Learn to identify and create dilations of figures with vocabulary like center of dilation. Understand the concept through examples and activities in this course. Engage in warm-up problems and daily challenges to master dilations in a fun way.

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Understanding Dilations: Enlargement & Reduction in Plane Figures

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  1. 5-6 Dilations Course 3 Warm Up Problem of the Day Lesson Presentation

  2. 5-6 Dilations 3 4 3 4 3 4 3 4 Course 3 Warm Up Multiply. 1. 4  2. 12  3. 24  4. –36  9 3 18 –27 10 30 5. 4 2.5 6. 12 2.5

  3. 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.

  4. Learn to identify and create dilations of plane figures.

  5. Vocabulary dilation center of dilation

  6. 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.

  7. 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.

  8. Additional Example 1: 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.

  9. Additional Example 1: 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.

  10. A' A A' B' B B' C C' C' A B C Check It Out: Example 1 Tell whether each transformation is a dilation. A. B. The transformation is not a dilation. The figure is distorted. The transformation is a dilation.

  11. A A A' A' B C C' B' B C C' B' Check It Out: Example 1 Tell whether each transformation is a dilation. D. C. The transformation is not a dilation. The figure is distorted. The transformation is a dilation.

  12. 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.

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

  14. 5-6 Dilations Helpful Hint A scale factor between 0 and 1 reduces a figure. A scale factor greater than 1 enlarges it. Course 3 Insert Lesson Title Here

  15. A’B’C’ 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) ABC 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. The vertices of the image are A’(8, 16), B’(6, 4), and C’(10, 4).

  16. 1 3 Multiply the coordinates by to find the vertices of the image. A’B’C’ C(6, 3) C’(6  , 3 ) C’(2, 1) B(9, 6) B’(9  , 6 ) B’(3, 2) A(3, 9) A’(3  , 9 ) A’(1, 3) ABC 1 3 1 3 1 3 1 3 1 3 1 3 1 3 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? The vertices of the image are A’(1, 3), B’(3, 2), and C’(2, 1).

  17. Check It Out: 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 10 8 4 6 2 0

  18. A’B’C’ 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 Check It Out: Example 3A Continued The vertices of the image are A’(4, 4), B’(8, 4), and C’(4, 8).

  19. C’ B’ A’ Check It Out: Example 3A Continued 10 8 6 C 4 2 B A 10 8 4 6 2 0

  20. Check It Out: Example 3B Dilate the figure by a scale factor of 0.5. What are the vertices of the image? 10 C 8 6 B A 4 2 10 8 4 6 2 0

  21. 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) A’B’C’ ABC C(4, 9) C’(4  0.5, 9  0.5) C’(2, 4.5) Check It Out: Example 3B Continued The vertices of the image are A’(2, 2.5), B’(4, 2.5), and C’(2, 4.5).

  22. C’ B’ A’ Check It Out: Example 3B Continued 10 C 8 6 B A 4 2 10 8 4 6 2 0

  23. 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 C’ C A B B’ A’ Lesson Quiz yes 2 4 6 2. Dilate the figure by a scale factor of 1.5 with P as the center of dilation. -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 A’(4,8) B’(10,12) C’(12,2)

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