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 coordi

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Thu Dec 03, 2020 2:45 pm

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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: Beat The GMAT — Problem Solving | Thu Dec 03, 2020 2:45 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: 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 co

by Brent@GMATPrepNow » Sun Dec 06, 2020 2:29 pm

BTGModeratorVI wrote: ↑
Thu Dec 03, 2020 2:45 pm
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

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8155; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: 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 co

by Scott@TargetTestPrep » Tue Dec 08, 2020 11:10 am

BTGModeratorVI wrote: ↑
Thu Dec 03, 2020 2:45 pm
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

Solution:

We use the midpoint formula: (x_1 + x_2)/2 = x-coordinate of the midpoint and (y_1 + y_2)/2 = y-coordinate of the midpoint.

We know that the coordinates of P are (r, s), and 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
Founder and CEO
[email protected]

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