Question

If square ABCD is defined by the coordinates A(0, 0), B(0, -5), C(-5, -5), D(-5, 0) is dilated by a scale factor of 2, with resulting vertex A' at (5, 5). What is the center of the dilation?

Answer 1

If the center of dilation is point O, then A is the midpoint of OA' and O is
O = 2A -A' = 2(0, 0) -(5, 5)
O = (-5, -5)

This coincides with point C.