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Find the missing vertex

Source: AHSME 1963 Problem 12

January 9, 2014
geometryparallelogramanalytic geometryAMC

Problem Statement

Three vertices of parallelogram PQRSPQRS are P(−3,−2)P(-3,-2), Q(1,−5)Q(1,-5), R(9,1)R(9,1) with PP and RR diagonally opposite. The sum of the coordinates of vertex SS is:
<spanclass=′latex−bold′>(A)</span> 13<spanclass=′latex−bold′>(B)</span> 12<spanclass=′latex−bold′>(C)</span> 11<spanclass=′latex−bold′>(D)</span> 10<spanclass=′latex−bold′>(E)</span> 9<span class='latex-bold'>(A)</span>\ 13 \qquad <span class='latex-bold'>(B)</span>\ 12 \qquad <span class='latex-bold'>(C)</span>\ 11 \qquad <span class='latex-bold'>(D)</span>\ 10 \qquad <span class='latex-bold'>(E)</span>\ 9
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