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Mock AIME 6 2006-2007 Problems/Problem 10

Revision as of 09:24, 23 November 2023 by Tomasdiaz (talk | contribs) (Created page with "==Problem== Given a point <math>P</math> in the coordinate plane, let <math>T_k(P)</math> be the <math>90^\circ</math> rotation of <math>P</math> around the point <math>(2000-...")
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Problem

Given a point $P$ in the coordinate plane, let $T_k(P)$ be the $90^\circ$ rotation of $P$ around the point $(2000-k,k)$. Let $P_0$ be the point $(2007,0)$ and $P_{n+1}=T_n(P_n)$ for all integers $n\ge 0$. If $P_m$ has a $y$-coordinate of $433$, what is $m$?

Solution

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