2011 BAMO 4 symmetric point construction using only straightedge
Source:
August 27, 2019
geometrystraightedgeconstruction
Problem Statement
In a plane, we are given line , two points and neither of which lies on line , and the reflection of point across line . Using only a straightedge, construct the reflection of point across line .
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.)