2014 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 9
Suppose that is a mapping of the plane into itself such that the vertices of every equilateral triangle of side one are mapped onto the vertices of a congruent triangle. Show that the map is distance preserving, i.e., for all points and in the plane, where denotes the distance between the points and in the plane. In other words, if any two points that are one unit apart are mapped to points that are one unit apart, then any two points are mapped to two points that are the same distance as their pre-images.
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