Bunuel wrote:
In the rectangular coordinate system above, if ΔOPQ and ΔQRS have equal area, what are the coordinates of point R ?
(1)The coordinates of point P are (0,12).
(2) OP = OQ and QS = RS.
Attachment:
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Solution:Question Stem Analysis:We need to determine the coordinates of point R, given that right triangles OPQ and QRS have the same area.
Statement One Alone:Knowing only the coordinates of point P is not enough to determine the coordinates of R. Statement one alone is not sufficient.
Statement Two Alone:We see that both triangles are right isosceles triangles (i.e., they are each 45-45-90 triangles). However, we can’t determine the coordinates of R without knowing any coordinates of vertices such as P, Q and/or S. Statement two alone is not sufficient.
Statements One and Two Together:Since right triangle OPQ is isosceles and P = (0, 12), then Q = (12, 0). Since both right triangles are isosceles and they have the same area, OQ = QS and OP = SR. Since Q = (12, 0), then S = (24, 0) so that OQ = QS. We see that R has the same x-coordinate as S and since OP = SR, so R must have the same y-coordinate as P; therefore, R = (24, 12). Both statements together are sufficient.
Answer: C _________________
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