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

[BTGModeratorVI]

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)

Answer: E
Source: Official guide

[Jay@ManhattanReview]

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)

Answer: E
Source: Official guide

Let's assume that Point P lies in Quadrant 1; thus, r and s would be positive numbers, and Point Q would like in Quadrant 3. In Q3 the coordinates of any point are negative. So, the coordinates of Point Q is (–r, –s).

The correct answer: E

Hope this helps!

-Jay
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[Brent@GMATPrepNow]

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)

Answer: E
Source: Official guide

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




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



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



Answer: E

Cheers,
Brent

[Scott@TargetTestPrep]

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)

Answer: E
Source: Official guide

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