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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.

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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.

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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.

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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’

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

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

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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.

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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.

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Finding a Scale Factor The blue quadrilateral is a dilation image of the red quadrilateral. Describe the dilation.

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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)

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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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Take two minutes to list words that come to mind when you hear the word dilation. Enlarging or reducing a figure is called dilation.

Take two minutes to list words that come to mind when you hear the word dilation. Enlarging or reducing a figure is called dilation.

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