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Dilations in the Coordinate Plane

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What is a dilation? A better name is a projection. The hands differ only in size, so dilations produce similar figures. This dilation is an enlargement since the dilation makes the image larger. The original is called the pre-image and the projection is called the image. The “light source” of the projection is called the center of the dilation

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Dilations on the Coordinate Plane A dilation with its center at the origin (0,0) is obtained by multiplying the x and y coordinates of the pre-image points by the scale factor. We use the variable “k” to represent the scale factor. (x,y) -> (kx,ky) is the coordinate notation for a dilation centered at the origin. For us, k will be a positive number. When k is greater than 1, the dilation is an enlargement. When k is less than 1, the dilation is a reduction.

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Example Since ½ is less than 1, we know it will be a reduction before we even begin.) Pre-imageImage A(-2,4)A’(-1,2) B(6,8)B’(3,4) C(2,0)C’(1,0)

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Complete Worksheet 6.6A for tomorrow.

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