1999 AIME Problem 2

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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.