2001 AMC 12 Problems/Problem 20
Contents
[hide]Problem
Points , , , and lie in the first quadrant and are the vertices of quadrilateral . The quadrilateral formed by joining the midpoints of , , , and is a square. What is the sum of the coordinates of point ?
Solution
We already know two vertices of the square: and .
There are only two possibilities for the other vertices of the square: either they are and , or they are and . The second case would give us outside the first quadrant, hence the first case is the correct one. As is the midpoint of , we can compute , and .
Video Solution
https://www.youtube.com/watch?v=wR0mphUnhLc
See Also
2001 AMC 12 (Problems • Answer Key • Resources) | |
Preceded by Problem 19 |
Followed by Problem 21 |
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All AMC 12 Problems and Solutions |
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