2002 AMC 12B Problem 18

A point P is randomly selected from the rectangular region with vertices (0,0),(2,0),(2,1),(0,1). What is the probability that P is closer to the origin than it is to the point (3,1)?

\mathrm{(A)}\ \frac 12 \qquad\mathrm{(B)}\ \frac 23 \qquad\mathrm{(C)}\ \frac 34 \qquad\mathrm{(D)}\ \frac 45 \qquad\mathrm{(E)}\ 1

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.