MathDB
Points in a plane

Source: 1976 AHSME Problem 8

May 15, 2014
analytic geometryprobabilityAMC

Problem Statement

A point in the plane, both of whose rectangular coordinates are integers with absolute values less than or equal to four, is chosen at random, with all such points having an equal probability of being chosen. What is the probability that the distance from the point to the origin is at most two units?
<spanclass=latexbold>(A)</span>1381<spanclass=latexbold>(B)</span>1581<spanclass=latexbold>(C)</span>1364<spanclass=latexbold>(D)</span>π16<spanclass=latexbold>(E)</span>the square of a rational number<span class='latex-bold'>(A) </span>\frac{13}{81}\qquad<span class='latex-bold'>(B) </span>\frac{15}{81}\qquad<span class='latex-bold'>(C) </span>\frac{13}{64}\qquad<span class='latex-bold'>(D) </span>\frac{\pi}{16}\qquad <span class='latex-bold'>(E) </span>\text{the square of a rational number}