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1964 AMC 12 Question 17

AMC12 · 1964 AMC 12

Question 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 $O.$ 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:
  1. $(1)$ only
  2. $(2)$ only
  3. $(3)$ only
  4. $(1)$ or $(2)$ only
  5. all three