Question

The square shown is dilated by a scale factor of 2. The center of dilation is point C. Which shows the correct image, A’ ?

Point C is inside of square A.
Point C is inside of square A. Square A prime is double the size of square A prime.
Point C is inside of square A. Square A prime is half the size of square A prime.
Point C is inside of square A. Square A prime is half the size of square A prime.
Point C is inside of square A. Square A prime is half the size of square A prime.

Answer 1

The correct image A' is the one that is twice as large as A and lies farther from C in the same directions — i.e. every vertex P of A goes to P' with CP' = 2·CP.

How to check/construct:
- Draw rays from C through each vertex P of the original square.
- On each ray, mark P' so that CP' = 2·CP.
- Connect the P' points to get A'.

Coordinate formula (if helpful): if C = (cx,cy) and a vertex P = (x,y), then P' = (cx + 2(x−cx), cy + 2(y−cy)) = (2x − cx, 2y − cy).

So pick the choice that shows a square twice the size positioned so each vertex is on the ray from C through the corresponding original vertex at twice the distance.