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MathNet 2019-part-04 — 184 problems (EN–VI) Question 173

Math Olympiad Vault · MathNet 2019-part-04 — 184 problems (EN–VI)

Question 173

Let $(0,0)$, $(10,0)$, $(10,8)$, and $(0,8)$ be the vertices of a rectangle on the Cartesian plane. Two lines with slopes $-3$ and $3$ pass through the rectangle and divide the rectangle into three regions with the same area. If the lines intersect above the rectangle, find the coordinates of their point of intersection.