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Points P, Q, R

Source: 1964 AHSME Problem 17

August 23, 2013
geometryparallelogramtrapezoidAMC

Problem Statement

Given the distinct points P(x1,y1)P(x_1, y_1), Q(x2,y2)Q(x_2, y_2) and R(x1+x2,y1+y2)R(x_1+x_2, y_1+y_2). Line segments are drawn connecting these points to each other and to the origin 00. Of the three possibilities: (1) parallelogram (2) straight line (3) trapezoid, figure OPRQOPRQ, depending upon the location of the points P,Q,P, Q, and RR, can be:
<spanclass=′latex−bold′>(A)</span> (1) only<spanclass=′latex−bold′>(B)</span> (2) only<spanclass=′latex−bold′>(C)</span> (3) only<spanclass=′latex−bold′>(D)</span> (1) or (2) only<spanclass=′latex−bold′>(E)</span> all three <span class='latex-bold'>(A)</span>\ \text{(1) only}\qquad<span class='latex-bold'>(B)</span>\ \text{(2) only}\qquad<span class='latex-bold'>(C)</span>\ \text{(3) only}\qquad<span class='latex-bold'>(D)</span>\ \text{(1) or (2) only}\qquad<span class='latex-bold'>(E)</span>\ \text{all three}
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