2014 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 9
Problem
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.
Solution
See also
| 2014 UNM-PNM Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNM-PNM Problems and Solutions | ||
