Problem: Given the distinct points and . 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 , and , can be:
Answer Choices:
A. (1) only
B. (2) only
C. (3) only
D. (1) or (2) only
E. all three
Solution:
If and , the points lie in a straight line through . Other. wise, a parallelogram is formed with the midpoint of diagonal and the midpoint of diagonal OR (if the diagonals of a quadrilateral bisect each other, the figure is a parallelogram).