MathDB

Symmetric Cut

Source:

December 18, 2005

geometryparallelogramanalytic geometrygraphing linesslopeAMCAIME

Problem Statement

Consider the parallelogram with vertices

(10,45),

(10,114),

(28,153),

and

(28,84).

A line through the origin cuts this figure into two congruent polygons. The slope of the line is

m/n,

where

m

and

n

are relatively prime positive integers. Find

m+n.