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7-5

7-5. Dilations. Warm Up. Problem of the Day. Lesson Presentation. Pre-Algebra. 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. 3 4.

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7-5

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  1. 7-5 Dilations Warm Up Problem of the Day Lesson Presentation Pre-Algebra

  2. 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.

  3. 3 4 3 4 3 4 3 4 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

  4. Homework….

  5. DO YOU REMEMBER THIS?

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

  7. Today we will examine TRANSFORMATIONS

  8. I LIED TO YOU! The resulting figure or image, of a translation, rotation or reflection is congruent to the original figure.

  9. Now, we will examine yet another transformation called. Dilation

  10. 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.

  11. ……. the doctor may dilate your pupils, which makes them larger.

  12. Vocabulary dilation scale factor center of dilation

  13. 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.

  14. Helpful Hint A scale factor between 0 and 1 reduces a figure. A scale factor greater than 1 enlarges it.

  15. 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. Why?

  16. Additional Example 1A & 1B: 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.

  17. Additional Example 1C & 1D: 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.

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

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

  20. 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.

  21. 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.

  22. G 1 cm 1 cm 2 cm 2 cm F’ H’ 1 cm F H 2 cm Try This: 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.

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

  24. Dilate the figure in Example 3B by a scale factor of . What are the vertices of the image? 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 The vertices of the image are A’(1, 3), B’(3, 2), and C’(2, 1).

  25. Try This: 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

  26. 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 Try This: Example 3A Continued The vertices of the image are A’(4, 4), B’(8, 4), and C’(4, 8).

  27. C’ B’ A’ Try This: Example 3A Continued 10 8 6 C 4 2 B A 10 8 4 6 2 0

  28. Try This: 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

  29. 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) Try This: Example 3B Continued The vertices of the image are A’(2, 2.5), B’(4, 2.5), and C’(2, 4.5).

  30. C’ B’ A’ Try This: Example 3B Continued 10 C 8 6 B A 4 2 10 8 4 6 2 0

  31. 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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