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In the xy-plane, the origin O is the midpoint of line segment PQ. If t

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In the xy-plane, the origin O is the midpoint of line segment PQ. If t  [#permalink]

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New post 17 Jun 2017, 10:47
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In the xy-plane, 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 xy-plane, the origin O is the midpoint of line segment PQ. If t  [#permalink]

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New post 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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In the xy-plane, the origin O is the midpoint of line segment PQ. If t  [#permalink]

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New post 17 Jun 2017, 10:51
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AbdurRakib wrote:
In the xy-plane, 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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Re: In the xy-plane, the origin O is the midpoint of line segment PQ. If t  [#permalink]

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New post 17 Jun 2017, 13:46
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AbdurRakib wrote:
In the xy-plane, 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 xy-plane, the origin O is the midpoint of line segment PQ. If t  [#permalink]

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New post 19 Jul 2017, 11:39
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Hi there. Theoretically, what if point P were on the y-axis. 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 xy-plane, the origin O is the midpoint of line segment PQ. If t  [#permalink]

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New post 19 Jul 2017, 21:55
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brandmanrocks wrote:
Hi there. Theoretically, what if point P were on the y-axis. 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 xy-plane, the origin O is the midpoint of line segment PQ. If t  [#permalink]

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New post 15 Nov 2017, 16:53
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AbdurRakib wrote:
In the xy-plane, 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 xy-plane, the origin O is the midpoint of line segment PQ. If t  [#permalink]

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New post 20 Nov 2017, 18:03
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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).

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Re: In the xy-plane, the origin O is the midpoint of line segment PQ. If t  [#permalink]

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New post 23 Mar 2018, 04:18
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Bunuel could you please refer to some similar questions.
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Re: In the xy-plane, the origin O is the midpoint of line segment PQ. If t  [#permalink]

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New post 23 Mar 2018, 06:29
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sadikabid27 wrote:
Bunuel could you please refer to some similar questions.


Similar questions:
https://gmatclub.com/forum/line-segment ... 45733.html
https://gmatclub.com/forum/if-line-segm ... 48583.html
https://gmatclub.com/forum/a-b-c-and-d- ... 44581.html
https://gmatclub.com/forum/c-is-the-mid ... 44574.html
https://gmatclub.com/forum/a-b-c-are-po ... 47480.html
https://gmatclub.com/forum/if-q-is-the- ... 44524.html
https://gmatclub.com/forum/on-the-coord ... 59763.html
https://gmatclub.com/forum/in-the-coord ... 42080.html
https://gmatclub.com/forum/m31-200213.html
https://gmatclub.com/forum/line-m-lies- ... 98105.html
https://gmatclub.com/forum/if-r-and-s-a ... 91633.html
https://gmatclub.com/forum/m15-184051.html
https://gmatclub.com/forum/points-m-5-2 ... 27803.html

Hope it helps.
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Re: In the xy-plane, the origin O is the midpoint of line segment PQ. If t  [#permalink]

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New post 18 Oct 2018, 05:27
AbdurRakib wrote:
In the xy-plane, 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)



If you draw a point (r,s) in the first quadrant (top-right) of the cartesian plane, you will automatically see that the "opposite" point will be (-r,-s) which makes O the midpoint.
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Re: In the xy-plane, the origin O is the midpoint of line segment PQ. If t  [#permalink]

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New post 27 Feb 2019, 07:02
Bunuel wrote:
brandmanrocks wrote:
Hi there. Theoretically, what if point P were on the y-axis. 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.



Sorry I still don't get it.. Why 0 = -0?
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Re: In the xy-plane, the origin O is the midpoint of line segment PQ. If t  [#permalink]

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New post 01 Mar 2019, 18:21
mottagmat wrote:
Bunuel wrote:
brandmanrocks wrote:
Hi there. Theoretically, what if point P were on the y-axis. 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.



Sorry I still don't get it.. Why 0 = -0?


all real numbers can be divided into three categories: positive, negative and zero.
check out this link
thanks
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Re: In the xy-plane, the origin O is the midpoint of line segment PQ. If t  [#permalink]

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New post 16 Jun 2019, 09:24
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AbdurRakib wrote:
In the xy-plane, 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)


Let's sketch a line segment with midpoint at the origin and an endpoint at (r, s)
Image



We can now travel the SAME DISTANCES (from the origin) to ensure that the origin is the midpoint.
Image


From here, we can see that (-r, -s) are the coordinates of the other point.
Image


Answer: E

Cheers,
Brent
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Re: In the xy-plane, the origin O is the midpoint of line segment PQ. If t  [#permalink]

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New post 19 Jul 2019, 08:58
GMATPrepNow wrote:
AbdurRakib wrote:
In the xy-plane, 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)


Let's sketch a line segment with midpoint at the origin and an endpoint at (r, s)
Image



We can now travel the SAME DISTANCES (from the origin) to ensure that the origin is the midpoint.
Image


From here, we can see that (-r, -s) are the coordinates of the other point.
Image


Answer: E

Cheers,
Brent




Hello Brent,

I understand precisely the graph you showed.I had assumed the same.

However,I understand that segment of line PQ can be a simple x axis as well.

_______P(-r,-s)__________________O____________________Q(r,s).

and in this case option (D) since s=0 will always be true.

Upon reflecting further, I see the line PQ can be rotated across Origin and so ycoordinated doesnt necessarily have to be zero.

GMAT sets so beautiful traps .

Please let me know if you see any gap in my thinking :)
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Re: In the xy-plane, the origin O is the midpoint of line segment PQ. If t  [#permalink]

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New post 19 Jul 2019, 09:06
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prabsahi wrote:
Hello Brent,

I understand precisely the graph you showed.I had assumed the same.

However,I understand that segment of line PQ can be a simple x axis as well.

_______P(-r,-s)__________________O____________________Q(r,s).

and in this case option (D) since s=0 will always be true.

Upon reflecting further, I see the line PQ can be rotated across Origin and so ycoordinated doesnt necessarily have to be zero.

GMAT sets so beautiful traps .

Please let me know if you see any gap in my thinking :)


You're correct to say that the answer COULD be D (in that particular case), but the question is asking for the answer that must be true (in all cases).

Cheers,
Brent
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Re: In the xy-plane, the origin O is the midpoint of line segment PQ. If t  [#permalink]

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New post 19 Jul 2019, 09:09
GMATPrepNow wrote:
prabsahi wrote:
Hello Brent,

I understand precisely the graph you showed.I had assumed the same.

However,I understand that segment of line PQ can be a simple x axis as well.

_______P(-r,-s)__________________O____________________Q(r,s).

and in this case option (D) since s=0 will always be true.

Upon reflecting further, I see the line PQ can be rotated across Origin and so ycoordinated doesnt necessarily have to be zero.

GMAT sets so beautiful traps .

Please let me know if you see any gap in my thinking :)


You're correct to say that the answer COULD be D (in that particular case), but the question is asking for the answer that must be true (in all cases).

Cheers,
Brent




Thanks for confirming ..I guess that was one of the trap and purpose of this question :)
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Re: In the xy-plane, the origin O is the midpoint of line segment PQ. If t   [#permalink] 19 Jul 2019, 09:09
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