Answer:
Point E
Explanation:
Notice that point E is the only point where you can draw a straight line from E to A' to A, E to B' to B, etc. That is, the line doesn't have to turn or bend to reach these three points. This doesn't work with any other point, so you know E is the point of dilation.
You can more firmly determine this by looking at the ratios of the distances. Notice how E is the only point where the ratio from of E to A and E to A' is equal to the ratio from of E to B and E to B', and so on for each vertex of the quadrilateral.