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1987 AMC 12 #25 - Triangle in the Plane

Source:

January 1, 2012
analytic geometrygeometrylinear algebramatrixAMC

Problem Statement

ABCABC is a triangle: A=(0,0)A=(0,0), B=(36,15)B=(36,15) and both the coordinates of CC are integers. What is the minimum area △ABC\triangle ABC can have?
<spanclass=′latex−bold′>(A)</span> 12<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 32<spanclass=′latex−bold′>(D)</span> 132<spanclass=′latex−bold′>(E)</span> there is no minimum <span class='latex-bold'>(A)</span>\ \frac{1}{2} \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ \frac{3}{2} \qquad<span class='latex-bold'>(D)</span>\ \frac{13}{2} \qquad<span class='latex-bold'>(E)</span>\ \text{there is no minimum}
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