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Difference between revisions of "2011 AIME I Problems/Problem 3"

(Created page with 'Let <math>L</math> be the line with slope <math>\frac{5}{12}</math> that contains the point <math>A=(24,-1)</math>, and let <math>M</math> be the line perpendicular to line <math…')
(No difference)

Revision as of 15:30, 19 March 2011

Let $L$ be the line with slope $\frac{5}{12}$ that contains the point $A=(24,-1)$, and let $M$ be the line perpendicular to line $L$ that contains the point $B=(5,6)$. The original coordinate axes are erased, and line $L$ is made the $x$-axis and line $M$ the $y$-axis. In the new coordinate system, point $A$ is on the positive $x$-axis, and point $B$ is on the positive $y$-axis. The point $P$ with coordinates $(-14,27)$ in the original system has coordinates $(\alpha,\beta)$ in the new coordinate system. Find $\alpha+\beta$.

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