Corresponding points are \(A(1,1)\to~A'(3,3)\), \(B(1,3)\to~B'(3,9)\). What is the center of the dilation?

The dilation center lies on every line joining an original point to its image, so two independent correspondence pairs can locate it. We’ll write both correspondence-line equations, intersect them, and then verify the recovered point by checking that one common scale factor sends both original displacement vectors to their images.