MathDB
2011 BAMO 4 symmetric point construction using only straightedge

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August 27, 2019
geometrystraightedgeconstruction

Problem Statement

In a plane, we are given line \ell, two points AA and BB neither of which lies on line \ell, and the reflection A1A_1 of point AA across line \ell. Using only a straightedge, construct the reflection B1B_1 of point BB across line \ell. Prove that your construction works.
Note: “Using only a straightedge” means that you can perform only the following operations: (a) Given two points, you can construct the line through them. (b) Given two intersecting lines, you can construct their intersection point. (c) You can select (mark) points in the plane that lie on or off objects already drawn in the plane. (The only facts you can use about these points are which lines they are on or not on.)