2001 AMC 12 Problems/Problem 20
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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 
.
See Also
| 2001 AMC 12 (Problems • Resources) | ||
| Preceded by Problem 19 | Followed by Problem 21 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
