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1993 AMC 12 #28 - Triangles in the Coordinate Place

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January 3, 2012
analytic geometrygeometryAMC

Problem Statement

How many triangles with positive area are there whose vertices are points in the xyxy-plane whose coordinates are integers (x,y)(x,y) satisfying 1≤x≤41 \le x \le 4 and 1≤y≤41 \le y \le 4?
<spanclass=′latex−bold′>(A)</span> 496<spanclass=′latex−bold′>(B)</span> 500<spanclass=′latex−bold′>(C)</span> 512<spanclass=′latex−bold′>(D)</span> 516<spanclass=′latex−bold′>(E)</span> 560 <span class='latex-bold'>(A)</span>\ 496 \qquad<span class='latex-bold'>(B)</span>\ 500 \qquad<span class='latex-bold'>(C)</span>\ 512 \qquad<span class='latex-bold'>(D)</span>\ 516 \qquad<span class='latex-bold'>(E)</span>\ 560
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