1964 AHSME Problem 17

Given the distinct points P(x_1, y_1), Q(x_2, y_2) and R(x_1+x_2, y_1+y_2). Line segments are drawn connecting these points to each other and to the origin 0. Of the three possibilities: (1) parallelogram (2) straight line (3) trapezoid, figure OPRQ, depending upon the location of the points P, Q, and R, can be:

\textbf{(A)}\ \text{(1) only}\qquad \textbf{(B)}\ \text{(2) only}\qquad \textbf{(C)}\ \text{(3) only}\qquad \textbf{(D)}\ \text{(1) or (2) only}\qquad \textbf{(E)}\ \text{all three}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.