Dilations: (Stretching/Shrinking)  Dilations use a scale factor to reduce or enlarge shapes.  Every dilation has a center and a scale factor. Most of.

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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.

Finding a Dilation To find a dilation with center C and scale factor n, you can use the following two rules.  The image C is itself (meaning C’=C)  For any point R, R’ is on CR and CR’ = nCR.

How do we locate dilation images?  A dilation is a transformation who preimage and image are similar. A dilation is not an isometry.  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. A B C A’ B’ C’ D D’

Example 2:  F(-3, -3), O(3, 3), R(0, -3) Scale factor 1/3 F O R F’ O’ R’

Example 3:  T(-1, 0), H(1, 0), I(2, -2), S(-2, -2) Scale factor 4 TH I T’ H’ I’ S 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)

Graphing Dilation Images  Solution: The scale factor is 3, so use the rule: (x, y)  (3x, 3y). P(2,0)  P’(32, 30) or P’(6, 0). The correct answer is B. The correct answer is B. What are the coordinates for G’ and Z’?

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