Question

Point A is located at (2, 3). What is the location of A' given dilation with scale factor of 3 and a center of dilation at (-1, 6)?

Answer 1

A'(8, -3)

Explanation:

When the center of a dilation is not the origin, the location of a point A dilated about center C by scale factor k can be found as ...

A' = C + k(A -C) = kA +(1-k)C

That is, the distance from the center of dilation is multiplied by the scale factor.

For A(2, 3), k=3, C(-1, 6), the new point A' will be ...

A' = 3(2, 3) +(-2)(-1, 6) = (6, 9) +(2, -12)

A' = (8, -3)