Given two concentric circles (circles that have the same center point), with the inner circle having a radius of r1 and the outer one having a radius of

r2 as shown, give a dilation that would map the inner circle onto the outer

circle. Specify both the center of dilation and the scale factor.

The center of dilation has a coordinate of and the scale factor is . The transformation formula is .

Two circles are concentric when they share the same center () but they have different radii (), where corresponds to the radius of the smaller circle. By analytic geometry we know that circles are modeled after this formula:

    (1)

If we assume that the center of dilation is the center of both circles and the dilation use a scale factor of . Then, we have the following expression:

    (2)

The center of dilation has a coordinate of and the scale factor is . The transformation formula is .

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