Question

△ABC with vertices at A(−1,−1) , B(4,−4) , and C(2,−6) is dilated by a scale factor of 32 to create △A′B′C′ . The center of dilation is the point (5, −6) . What are the coordinates of vertex B′ ?

Answer 1

When D is the center of dilation, and k is the dilation factor, the image point is

... B' = k(B -D) +D

Filling in the given values, we have

... B' = 32((4, -4) -(5, -6)) +(5, -6)

... = 32(-1, 2) +(5, -6)

... = (-32, 64) +(5, -6)

... B' = (-27, 58)