Mock AIME 6 2006-2007 Problems/Problem 10
Problem
Given a point in the coordinate plane, let be the rotation of around the point . Let be the point and for all integers . If has a -coordinate of , what is ?
Solution
Let be the rotational matrix for a point along the origin:
For
Let be the point of rotation.
~Tomas Diaz. orders@tomasdiaz.com