Dilations with Center other than the Origin

A dilation with any point other than the origin as the center of dilation can be accomplished by first translating the center of dilation and figure so the origin becomes the center, and then translating back:

Example 7:  Find a coordinate rule for the dilation with center (5, –3) and scale factor 2.

Solution:  If (x, y) is a point on a figure to be dilated, we first translate left 5 and up 3.  This gives us the point (x – 5, y + 3), and the origin becomes the center of the dilation.  The dilation now gives us (2x – 10, 2y + 6).  Then we translate back--that is, right 5 and down 3, which gives us (2x – 10 + 5, 2y + 6 – 3).  So the coordinate rule is:

(x, y) --> (2x – 5, 2y + 3)

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