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.
Let's write in matrix form as:
~Tomas Diaz. orders@tomasdiaz.com