MathDB
Triangle Counting in a Grid

Source: 2017 AMC10A #23

February 8, 2017
AMCAMC 10AMC 10 A2017 AMC 10Acounting

Problem Statement

How many triangles with positive area have all their vertices at points (i,j)(i,j) in the coordinate plane, where ii and jj are integers between 11 and 55, inclusive?
<spanclass=latexbold>(A)</span> 2128<spanclass=latexbold>(B)</span> 2148<spanclass=latexbold>(C)</span> 2160<spanclass=latexbold>(D)</span> 2200<spanclass=latexbold>(E)</span> 2300<span class='latex-bold'>(A)</span>\ 2128 \qquad<span class='latex-bold'>(B)</span>\ 2148 \qquad<span class='latex-bold'>(C)</span>\ 2160 \qquad<span class='latex-bold'>(D)</span>\ 2200 \qquad<span class='latex-bold'>(E)</span>\ 2300