Question

Quadrilateral ABCD is translated up and to the right, and then rotated about point Q. Which congruency statement is correct?

ABCD ≅ WXYZ
ABCD ≅ ZYXW
ABCD ≅ WZYX
ABCD ≅ ZWXY

Answer 1

I can’t decide which of the four is correct without seeing the picture (or being told which image point each original vertex maps to). Give the diagram or tell me where A, B, C, D end up (which of W,X,Y,Z each corresponds to), and I’ll pick the right statement.

Key idea you can use yourself: translations and rotations are orientation‑preserving rigid motions. So the image of ABCD must appear in the same cyclic order (clockwise or counterclockwise). That means the only possible correct correspondences are cyclic shifts of ABCD:

- ABCD ≅ WXYZ
- ABCD ≅ XYZW
- ABCD ≅ YZWX
- ABCD ≅ ZWXY

Any correspondence that reverses the order (e.g. ZYXW or WZYX) would be a reflection and cannot result from only a translation + rotation. If you tell me which vertex A maps to (W, X, Y, or Z), I’ll give the exact congruence statement.