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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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Properties of Dilations, Day 2. How do you describe the properties of dilations? Dilations change the size of figures, but not their orientation or.

Properties of Dilations, Day 2. How do you describe the properties of dilations? Dilations change the size of figures, but not their orientation or.

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