Problem:
A square in the coordinate plane has vertices whose -coordinates are , and . What is the area of the square?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let the square have vertices in counterclockwise order. Without loss of generality assume that and for some . Because is the image of under a counterclockwise rotation about , the coordinates of are , so . Therefore the area of the square is . Note that , and is indeed a square.
The problems on this page are the property of the MAA's American Mathematics Competitions