MathDB
Particle Moves

Source: AIME 2008II Problem 9

April 3, 2008
analytic geometrygeometrygeometric transformationrotationlinear algebramatrixAMC

Problem Statement

A particle is located on the coordinate plane at (5,0) (5,0). Define a move for the particle as a counterclockwise rotation of π/4 \pi/4 radians about the origin followed by a translation of 10 10 units in the positive x x-direction. Given that the particle's position after 150 150 moves is (p,q) (p,q), find the greatest integer less than or equal to |p|\plus{}|q|.
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