1. UNIT IIA DAY 11 8.7 Dilations

2. Do Now What is the definition of rigid transformation? What is a scale factor?

3. Dilations A dilation is a nonrigid motion in which the image and preimage are similar.  A dilation has a center C and a scale factor k.

4. Dilations Every point P gets mapped to a point P ' so that… 1. P ' lies on line CP. 2. The scale factor k is a positive number such that k = ≠1. 3. Exception: The center point C gets mapped to itself. CP’ CP

5. Reduction/Enlargement The dilation is a reduction if 0 1.

6. Ex. 1: Identifying Dilations Identify the dilation as an enlargement or a reduction and find its scale factor.

7. Ex. 2: Dilation in a coordinate plane Draw a dilation of rectangle ABCD: A(2, 2), B(6, 2), C(6, 4), and D(2, 4). Use the origin as the center and a scale factor of ½.

8. Notes: In a coordinate plane, dilations whose centers are the origin have the property that the image of P(x, y) is P '(kx, ky).

9. Ex. 2A: Dilation in coordinate plane Draw a dilation of rectangle ABCD: A(2, 2), B(6, 2), C(6, 4), and D(2, 4). Use the origin as the center and a scale factor of ½. How does the perimeter of the preimage compare to the perimeter of the image?

10. Ex. 3: Real world The shadow is a dilation, or enlargement, of the shadow puppet. When looking at a cross sectional view, ∆LCP ~ ∆LSH.

11. Ex. 3 (Shadow Puppet) continued The shadow puppet shown is 12 inches tall (CP). Find the height of the shadow, SH, if the distance from the light to the puppet (LC or LP) is 59 inches and the distance from the light to the screen (LS or LH) is 74 inches. By what percent is the shadow larger than the puppet?

12. Ex. 3A (Shadow Puppet) continued What would happen to the shadow if the puppet moved closer to the screen (i.e., farther from the light)? Repeat the problem for LC = LP = 66 in. and LS = LH = 74 in.

13. Closure How are the coordinates of the vertex of a figure related to the coordinates of the vertex of the image after a dilation with center at the origin?