MathDB
A Triangle in the Cartesian Plane

Source:

June 13, 2009
analytic geometrygeometry

Problem Statement

A triangle is formed by joining three points whose coordinates are integers. If the x x-coordinate and the y y-coordinate each have a value of 1 1, then the area of the triangle, in square units: <spanclass=latexbold>(A)</span> must be an integer<spanclass=latexbold>(B)</span> may be irrational<spanclass=latexbold>(C)</span> must be irrational<spanclass=latexbold>(D)</span> must be rational<spanclass=latexbold>(E)</span> will be an integer only if the triangle is equilateral. <span class='latex-bold'>(A)</span>\ \text{must be an integer}\qquad <span class='latex-bold'>(B)</span>\ \text{may be irrational}\qquad <span class='latex-bold'>(C)</span>\ \text{must be irrational}\qquad <span class='latex-bold'>(D)</span>\ \text{must be rational}\qquad \\ <span class='latex-bold'>(E)</span>\ \text{will be an integer only if the triangle is equilateral.}