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Random Point

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January 2, 2009
probabilitygeometryrectangletrapezoidperpendicular bisector

Problem Statement

A point P P is randomly selected from the rectangular region with vertices (0,0) (0, 0), (2,0) (2, 0), (2,1) (2, 1), (0,1) (0, 1). What is the probability that P P is closer to the origin than it is to the point (3,1) (3, 1)? <spanclass=′latex−bold′>(A)</span> 12<spanclass=′latex−bold′>(B)</span> 23<spanclass=′latex−bold′>(C)</span> 34<spanclass=′latex−bold′>(D)</span> 45<spanclass=′latex−bold′>(E)</span> 1 <span class='latex-bold'>(A)</span>\ \frac{1}{2} \qquad <span class='latex-bold'>(B)</span>\ \frac{2}{3} \qquad <span class='latex-bold'>(C)</span>\ \frac{3}{4} \qquad <span class='latex-bold'>(D)</span>\ \frac{4}{5} \qquad <span class='latex-bold'>(E)</span>\ 1
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