A dilation makes a figure larger or smaller, but has the same shape as the original. In other words, the dilation is similar to the original. All dilations have a center and a scale factor. The center is the point of reference for the dilation (like the vanishing point in a perspective drawing) and scale factor tells us how much the figure stretches or shrinks. A scale factor is typically labeled k and is always greater than zero. Also, if the original figure is labeled △ABC, for example, the dilation would be △A′B′C′. The ′ mark indicates that it is a copy. This tic mark is said “prime,” so A′ is read “A-prime.” A second dilation would be A′′, read “A double-prime.”
If the dilated image is smaller than the original, then the scale factor is 0<k<1.
If the dilated image is larger than the original, then the scale factor is k>1.
To dilate something in the coordinate plane, multiply each coordinate by the scale factor. This is called mapping. For any dilation the mapping will be (x,y)→(kx,ky). In this Concept, the center of dilation will always be the origin, unless otherwise stated.
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