D, E and F are the midpoints of BC, CA, and AB respectively. A dilation maps triangle ABC to triangle AFE. What is the scale factor of this dilation?
E is the midpoint of AC, so AE is half the length of AC, or AE = 1/2 * AC
One way to find the scale factor from △ABC to △AFE is to find AE / AC
AE / AC = (1/2 * AC) / AC = 1/2
So the scale factor is 1/2
(Remember the scale factor is the number which each side of the starting triangle must be multiplied by in order to make it the same size as the "goal" triangle. In this case, each side of △ABC must be multiplied by 1/2 to make it the same size as △AFE.)