2008 AMC 12A Problems/Problem 25
Problem
A sequence , , , of points in the coordinate plane satisfies
for .
Suppose that . What is ?
Solution
This sequence can also be expressed using matrix multiplication as follows:
.
Thus, is formed by rotating counter-clockwise about the origin by and dilating the point's position with respect to the origin by a factor of .
So, starting with and performing the above operations times in reverse yields .
Rotating clockwise by yields . A dilation by a factor of yields the point .
Therefore, .
See Also
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