1999 AIME Problems/Problem 2
Contents
[hide]Problem
Consider the parallelogram with vertices , , , and . A line through the origin cuts this figure into two congruent polygons. The slope of the line is where and are relatively prime positive integers. Find .
Solution
Solution 1
Let the first point on the line be where a is the height above . Let the second point on the line be . For two given points, the line will pass the origin iff the coordinates are proportional (such that ). Then, we can write that . Solving for yields that , so . The slope of the line (since it passes through the origin) is , and the solution is .
See also
1999 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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