Question

triangle XYZ is drawn on a coordinate plane with vertices X(0,4), Y(2,0), and Z(4,7) if you dilate the triangle to form triangle X'Y'Z' using a magnitude of 1/2 and a center of dilation at (4,7) what are the coordinate points of the new vertices

Answer 1

Use the dilation formula about center C = (4,7): X' = C + k*(X - C) with k = 1/2.

- X' = (4 + 1/2*(0-4), 7 + 1/2*(4-7)) = (2, 5.5) = (2, 11/2)
- Y' = (4 + 1/2*(2-4), 7 + 1/2*(0-7)) = (3, 3.5) = (3, 7/2)
- Z' = (4 + 1/2*(4-4), 7 + 1/2*(7-7)) = (4, 7)

So X'(2, 11/2), Y'(3, 7/2), Z'(4, 7).