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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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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)
[Reveal] Spoiler: OA

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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, 09:51
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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In the xy-plane, the origin O is the midpoint of line segment PQ. If t [#permalink]

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

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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, 10:39
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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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, 15:53
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, 17:03
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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).

Final Answer:
[Reveal] Spoiler:
E


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Re: In the xy-plane, the origin O is the midpoint of line segment PQ. If t   [#permalink] 20 Nov 2017, 17:03
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