combo geo, with reflections on broken line ABCD
Source: TOT 346 1992 Autumn A J4 - Tournament of Towns
June 10, 2024
geometrygeometric transformationreflectionbroken linecombinatoricscombinatorial geometry
Problem Statement
On the plane is give a broken line in which , and is not equal to . The positions of and are fixed but and change their positions in turn according to the following rule (preserving the distance rules given): the point is reflected with respect to the line , then is reflected with respect to the line (in which occupies its new position), then is reflected with respect to the line ( occupying its new position), is reflected with respect to the line , and so on. Prove that after several steps and coincide with their initial positions.(M Kontzewich)