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In the rectangular coordinate system above, if ΔOPQ and ΔQRS have equa [#permalink]
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06 Oct 2016, 05:17
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Re: In the rectangular coordinate system above, if ΔOPQ and ΔQRS have equa [#permalink]
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06 Oct 2016, 07:56
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ΔOPQ and ΔQRS have equal area > 0.5*OP*OQ = 0.5*QS*RS
St1: The coordinates of point P are (0,12) > OP = 12 12*OQ = QS*RS Clearly insufficient as we do not know the lengths of OQ, QS and RS.
St2: OP = OQ and QS = RS > Not Sufficient as we do not know the values of the given lengths
Combining St1 and St2: OP^2 = QS^2 > OP = QS Hence OP = OQ = QS = RS = 12 Coordinates of R = (24,12) Sufficient
Answer: C



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Re: In the rectangular coordinate system above, if ΔOPQ and ΔQRS have equa [#permalink]
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06 Oct 2016, 08:04
Vyshak wrote: ΔOPQ and ΔQRS have equal area > 0.5*OP*OQ = 0.5*QS*RS
St1: The coordinates of point P are (0,12) > OP = 12 12*OQ = QS*RS Clearly insufficient as we do not know the lengths of OQ, QS and RS.
St2: OP = OQ and QS = RS > Not Sufficient as we do not know the values of the given lengths
Combining St1 and St2: OP^2 = QS^2 > OP = QS Hence OP = OQ = QS = RS = 12 Coordinates of R = (24,12) Sufficient
Answer: C Agree with Vyshak's explanation. Answer must be C.



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Re: In the rectangular coordinate system above, if ΔOPQ and ΔQRS have equa [#permalink]
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06 Oct 2016, 08:30
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: 20161006_1616.png Statement 1 gives only y coordinate value. Without knowing the distance OS we cannot find the coordinate of point R. In Suff.. Statement 2 says both the triangles are isosceles but this data is not suff to find the coordinates. In Suff Combining we have x coordinate of R as 24 and y coordinate of R as 12 R (24,12) Hence C



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Re: In the rectangular coordinate system above, if ΔOPQ and ΔQRS have equa [#permalink]
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09 Jul 2017, 22:34
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: 20161006_1616.png Hi I request you to please solve this question. Given below the solution, I couldn't get how op^2 = QS^2



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Re: In the rectangular coordinate system above, if ΔOPQ and ΔQRS have equa [#permalink]
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09 Jul 2017, 23:29
rajatbanik wrote: 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: 20161006_1616.png Hi I request you to please solve this question. Given below the solution, I couldn't get how op^2 = QS^2 In the rectangular coordinate system above, if ΔOPQ and ΔQRS have equal area, what are the coordinates of point R ? Since ΔOPQ and ΔQRS have equal area, then \(\frac{1}{2}*OP*OQ = \frac{1}{2}*RS*QS\), which gives \(OP*OQ = RS*QS\). (1) The coordinates of point P are (0,12). This implies that OP = 12. Not sufficient. (2) OP = OQ and QS = RS. No values are given, so this statement is clearly insufficient. But from this statement we get that \(OP^2 = RS^2\) (from \(OP*OQ = RS*QS\)), which gives OP = RS. So, OP = OQ = QS = RS. Basically we get that ΔOPQ and ΔQRS are congruent, similar triangles. (1)+(2) \(OP^2 = RS^2=12^2\). So, \(OP = OQ = QS = RS=12\). Thus the coordinates of R are (24, 12). Sufficient. Answer: C.
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Re: In the rectangular coordinate system above, if ΔOPQ and ΔQRS have equa [#permalink]
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15 Jul 2017, 04:50
For statement 1, can't a pythagorean triplet apply? That way A is also sufficient. (12,13,5) B) is sufficient on its own too, giving us triangle 1 with (0,0) (0,12) and since two sides are equal, (12,0)for the coordinate Q. And since we have (12,0) we get 24,0 and the last coordinate of R
Could someone explain why D is wrong? And what is the error in the above logic?



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In the rectangular coordinate system above, if ΔOPQ and ΔQRS have equa [#permalink]
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09 Aug 2017, 23:08
\sqrt{} Madhavi1990 wrote: For statement 1, can't a pythagorean triplet apply? That way A is also sufficient. (12,13,5) B) is sufficient on its own too, giving us triangle 1 with (0,0) (0,12) and since two sides are equal, (12,0)for the coordinate Q. And since we have (12,0) we get 24,0 and the last coordinate of R
Could someone explain why D is wrong? And what is the error in the above logic? For (1) infinitely many other cases are possible. For example, (12, 1, \(\sqrt{145}\)), (12, 2, \(\sqrt{148}\)), (12, 1.5, \(\sqrt{146.25}\)), ... Generally knowing only one side of a triangle is not enough to find other sides. For (2) no values are given. You cannot use info from one statement when solving another.
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In the rectangular coordinate system above, if ΔOPQ and ΔQRS have equa
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