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

This topic has expert replies
Legendary Member
Posts: 1223
Joined: Sat Feb 15, 2020 2:23 pm
Followed by:1 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members
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
_________________
Manhattan Review Test Prep

Locations: Manhattan Review Bangalore | Free GRE Practice Test | GRE Prep Hyderabad | Kukatpally GRE Coaching | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770
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)
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
Brent Hanneson - Creator of GMATPrepNow.com
Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8086
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members
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
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage