1995 AHSME Problems/Problem 21
Problem
Two nonadjacent vertices of a rectangle are and , and the coordinates of the other two vertices are integers. The number of such rectangles is
Solution
The center of the rectangle is , and the distance from the center to a corner is . The remaining two vertices of the rectangle must be another pair of points opposite each other on the circle of radius 5 centered at the origin. Let these points have the form , where . This equation has six pairs of integer solutions: , , , , , and . The first pair of solutions are the endpoints of the given diagonal, and the other diagonal must span one of the other five pairs of points.
See also
1995 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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