Dilations: (Stretching/Shrinking). Dilations use a scale factor to reduce or enlarge shapes. Every dilation has a center and a scale factor. Most of the time it is the origin (0, 0) Scale Factor: tells you how many times larger or smaller your image will be.
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Dilations: (Stretching/Shrinking) • Dilations use a scale factor to reduce or enlarge shapes. • Every dilation has a center and a scale factor. Most of the time it is the origin (0, 0) • Scale Factor: tells you how many times larger or smaller your image will be. • The new shape and the image are similar. Dilations are also called similarity transformations.
How do we locate dilation images? • A dilation is a transformation whose preimage and image are similar. • Every dilation has a center and a scale factor n, n >0. The scale factor describes the size change from the original figure to the image.
Example 1: • Quadrilateral ABCD has vertices A(-2, -1), B(-2, 1), C(2, 1) and D(1, -1). • Find the coordinates of the image for the dilation with a scale factor of 2 and center of dilation at the origin. C’ B’ B C A D A’ D’
F(-3, -3), O(3, 3), R(0, -3) Scale factor 1/3 Example 2: O O’ F’ R’ F R
T(-1, 0), H(1, 0), I(2, -2), S(-2, -2) Scale factor 4 Example 3: T H H’ T’ S I I’ S’
The dilation is an enlargement if the scale factor is > 1. The dilation is a reduction if the scale factor is between 0 and 1.
Finding a Scale Factor • The blue triangle is a dilation image of the red triangle. Describe the dilation. • The center is X. The image is larger than the preimage, so the dilation is an enlargement.
Finding a Scale Factor • The blue quadrilateral is a dilation image of the red quadrilateral. Describe the dilation.
Graphing Dilation Images • ∆PZG has vertices P(2,0), Z(-1, ½), and G (1, -2). What are the coordinates of the image of P for a dilation with center (0,0) and scale factor 3? a) (5, 3) b) (6,0) c) (2/3, 0) d) (3, -6)
Solution: The scale factor is 3, so use the rule: (x, y)(3x, 3y). P(2,0) P’(3•2, 3•0) or P’(6, 0). The correct answer is B. What are the coordinates for G’ and Z’? Graphing Dilation Images