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In the xyplane, the origin O is the midpoint of line segment PQ. If t [#permalink]
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17 Jun 2017, 10:47
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In the xyplane, the origin O is the midpoint of line segment PQ. If the coordinates of P are (r,s), what are the coordinates of Q ? A. (r,s) B. (s,–r) C. (–s,–r) D. (–r,s) E. (–r,–s)
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In the xyplane, the origin O is the midpoint of line segment PQ. If t [#permalink]
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17 Jun 2017, 10:51
AbdurRakib wrote: In the xyplane, the origin O is the midpoint of line segment PQ. If the coordinates of P are (r,s), what are the coordinates of Q ?
A. (r,s) B. (s,–r) C. (–s,–r) D. (–r,s) E. (–r,–s) Given coordinates of P are (r,s) and origin O is midpoint of line segment PQ. Therefore Line PQ falls in I and III quadrants.
Both x and y coordinates will be have same value but negative sign.
Therefore coordinates of Q would be (r,s). Answer (E)...



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In the xyplane, the origin O is the midpoint of line segment PQ. If t [#permalink]
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17 Jun 2017, 11:02
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Given that one of the points on the line segment(PQ) is P(r,s) and the midpoint is the origin(0,0) We need to find out the coordinates of the other point Q Midpoint of 2 points(x1,y1) and (x2,y2) is ((x1+x2)/2,(y1+y2)/2) Since we have one point P(r,s) x1=r and midpoint is (0,0) r+x2/2 = 0. This is possible when x2=r s+y2/2 = 0. This is possible when y2=s Hence point Q has coordinates (r,s) which is Option E
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Re: In the xyplane, the origin O is the midpoint of line segment PQ. If t [#permalink]
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17 Jun 2017, 13:46
AbdurRakib wrote: In the xyplane, the origin O is the midpoint of line segment PQ. If the coordinates of P are (r,s), what are the coordinates of Q ?
A. (r,s) B. (s,–r) C. (–s,–r) D. (–r,s) E. (–r,–s) This can be solved by assuming values. If P(r, s) = P(2, 2) then Q must be at the other end of the diagonal through the origin, so at (2, 2), which is (r, s). Answer: E.
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In the xyplane, the origin O is the midpoint of line segment PQ. If t [#permalink]
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19 Jul 2017, 11:39
Hi there. Theoretically, what if point P were on the yaxis. If O is at the origin then wouldn't the other endpoint Q be (r, s)? For example, if P is (3,0) then Q would be (3,0). In this case, (r,s) could be (r,s). This reason I bring this up is that I can find a case (line PQ runs along the axis) in which point Q may not necessarily be equal to (r,s) if one of the end points are on an axis. Thanks!



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Re: In the xyplane, the origin O is the midpoint of line segment PQ. If t [#permalink]
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19 Jul 2017, 21:55
brandmanrocks wrote: Hi there. Theoretically, what if point P were on the yaxis. If O is at the origin then wouldn't the other endpoint Q be (r, s)? For example, if P is (3,0) then Q would be (3,0). In this case, (r,s) could be (r,s). This reason I bring this up is that I can find a case (line PQ runs along the axis) in which point Q may not necessarily be equal to (r,s) if one of the end points are on an axis. Thanks! If P is (3, 0), then yes Q will be (3, 0) but it's still (r, s) because 0 =  0.
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Re: In the xyplane, the origin O is the midpoint of line segment PQ. If t [#permalink]
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15 Nov 2017, 16:53
AbdurRakib wrote: In the xyplane, the origin O is the midpoint of line segment PQ. If the coordinates of P are (r,s), what are the coordinates of Q ?
A. (r,s) B. (s,–r) C. (–s,–r) D. (–r,s) E. (–r,–s) We can let the coordinates of Q be (x, y). Since the origin (0, 0) is the midpoint of PQ, we have: (r + x)/2 = 0 and (s + y)/2 = 0 Multiplying each equation by 2, we have: r + x = 0 and s + y = 0 x = r and y = s Thus, the coordinates of Q are (r, s). Answer: E
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Re: In the xyplane, the origin O is the midpoint of line segment PQ. If t [#permalink]
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20 Nov 2017, 18:03
Hi All, We're told that the origin O is the MIDPOINT of line segment PQ and that the coordinates of P are (r,s). We're asked for the coordinates of Q. This question can be solved by TESTing VALUES. IF... Point P = (r,s) = (2,1)... then Point Q would be (2, 1). That equates to (r,s). Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: In the xyplane, the origin O is the midpoint of line segment PQ. If t
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