1999 AIME Problems/Problem 2
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
Let the first point on the line x=10 be (10,45+x) where x is the height above (10,45). Let the second point (on the line x=28) be (28, 153-x). Since for a line to pass through the origin, and for two points (x,y) and (w,z) then . Then 10(153-x)=28(45+x) and
(needs to be finished)