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Using only a ruler and a compass, find the origin of the coordinate system.

Source: Serbia JBMO TST 2012

October 6, 2023
functionanalytic geometry

Problem Statement

In a coordinate system there are drawn the graphs of the functions y=ax+by=ax+b and y=bx+a,(a≠b)y=bx+a, (a\neq b). Their intersection is marked with red and their intersections with the OyOy axis are marked with blue. Everything is erased except the marked points. Using only a ruler and a compass, find the origin of the coordinate system.
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