2. 外语
  3. Parallelogram OPQR lies in the xy-plane, as shown in the figure above. The coordinates of point P are(2,4)and the coordinates of

Parallelogram OPQR lies in the xy-plane, as shown in the figure above. The coordinates of point P are(2,4)and the coordinates of

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问题
Parallelogram OPQR lies in the xy-plane, as shown in the figure above. The coordinates of point P are(2,4)and the coordinates of point Q are(8, 6). What are the coordinates of point R ?
选项 A、(3,2)
B、(3,3)
C、(4,4)
D、(5,2)
E、(6,2)
答案E
解析
    Since OPQR is a parallelogram, line segments PQ and OR have the same length and the same slope. Therefore, in the figure above, PQM and ORN arc congruent right triangles. From the coordinates of P and Q, the lengths of the legs of triangle PQM are PM = 8 - 2 = 6 and QM = 6-4 = 2. Thus, the lengths of the legs ON and RN of triangle ORN are also 6 and 2, respectively. So the coordinates of point R are(6, 2). The correct answer is Choice E.
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