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

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by BTGModeratorVI » Wed Apr 22, 2020 11:08 am

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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)

Answer: E
Source: Official guide
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Source: — Problem Solving |

BTGModeratorVI wrote:
Wed Apr 22, 2020 11:08 am
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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BTGModeratorVI wrote:
Wed Apr 22, 2020 11:08 am
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)
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We can now travel the SAME DISTANCES (from the origin) to ensure that the origin is the midpoint.
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From here, we can see that (-r, -s) are the coordinates of the other point.
Image


Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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BTGModeratorVI wrote:
Wed Apr 22, 2020 11:08 am
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

Scott Woodbury-Stewart
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