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Geometry

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Geometry

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  1. Section 8.7 Notes Geometry

  2. 8.7 Dilations • A Dilation is a transformation that either enlarges or reduces the size of a figure, with respect to a center point, A.

  3. 8.7 Dilations • If the image is smaller, then it is a reduction and the scale factor is less than 1, (k < 1) • *Note: the distance that correlates to the image is always the numerator

  4. 8.7 Dilations • If the image is larger, then it is an enlargement and the scale factor is greater than 1, (k > 1)

  5. Is the dilation a reduction or enlargment? • Reduction • Enlargment 10 0 of 24

  6. Is the dilation a reduction or enlargement? • Reduction • Enlargement 10 0 of 24

  7. Is the dilation a reduction or enlargement? • Reduction • Enlargement 8 0 of 24

  8. Find the scale factor of the dilation • 5 • 2 • ½ • 1/5

  9. Find the scale factor of the dilation • 4 • 3/2 • 2/3 • 1/4

  10. Find the scale factor of the dilation • 5 • 9/4 • 4/9 • x/3

  11. Find the value of x. • 8 • 16.5 • 17 • 20

  12. Find the value of x. • 4 • 8 • 9 • 12

  13. 8.7 Dilations • Dilations in the coordinate plane, with the origin as the center of dilation, can be done by multiplying the coordinates by the scale factor. • In general for a dilation, (x , y)  (k*x, k*y) • Ex. The center of dilation is the origin and the scale factor is k = 4, then (3, -2)  (12, -8)

  14. What is the image of (4, 8), using the scale factor k = 2 • (2, 4) • (1, 2) • (8, 16) • (6, 10)

  15. What is the image of L, dilated with scale factor k = ½ • (1.5, 0) • (2.5, 0) • (3 , 0) • (6 , 0)