2014 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 9

Problem

Suppose that $f$ 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 $f$ is distance preserving, i.e., $d(p, q) = d(f(p), f(q))$ for all points $p$ and $q$ in the plane, where $d(x, y)$ denotes the distance between the points $x$ and $y$ 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.

Solution

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See also

2014 UNM-PNM Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 8
Followed by
Problem 10
1 2 3 4 5 6 7 8 9 10
All UNM-PNM Problems and Solutions
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