Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on A Parallelogram and a Line.
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 \(\frac{m}{n}\), where m and n are relatively prime positive integers, find m+n.
Parallelogram
Slope of line
Integers
Answer: is 118.
AIME I, 1999, Question 2
Geometry Vol I to IV by Hall and Stevens
By construction here we see that a line makes the parallelogram into two congruent polygons gives line passes through the centre of the parallelogram
Centre of the parallogram is midpoint of (10,45) and (28,153)=(19,99)
Slope of line =\(\frac{99}{19}\) then m+n=118.
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