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O(0,0) construction given A (1, 2) ,B (3,1) (2019 Kyiv City MO Round2 7.3.1)

Source:

September 17, 2020
geometryconstructionanalytic geometrypointscoordinate geometry

Problem Statement

The teacher drew a coordinate plane on the board and marked some points on this plane. Unfortunately, Vasya's second-grader, who was on duty, erased almost the entire drawing, except for two points A(1,2)A (1, 2) and B(3,1)B (3,1). Will the excellent Andriyko be able to follow these two points to construct the beginning of the coordinate system point O(0,0)O (0, 0)? Point A on the board located above and to the left of point BB.