2001 AIME II Problems/Problem 4
Problem
Let . The lines whose equations are and contain points and , respectively, such that is the midpoint of . The length of equals , where and are relatively prime positive integers. Find .
Solution
The coordinates of can be written as and the coordinates of point can be written as . By the midpoint formula, we have and . Solving for gives , so the point is . The answer is twice the distance from to , which by the distance formula is . Thus, the answer is .
See also
2001 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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