a & b are positive numbers. What are the co-ordinates of midpoint of segment CD in xy plane?
1) co-ordinates of C are (a,1-b)
2) co-ordinates of D are (1-a,b)
Co-ordinate Geometry
This topic has expert replies
-
- Senior | Next Rank: 100 Posts
- Posts: 44
- Joined: Thu Jan 03, 2013 10:30 pm
- Thanked: 4 times
GMAT/MBA Expert
- Anurag@Gurome
- GMAT Instructor
- Posts: 3835
- Joined: Fri Apr 02, 2010 10:00 pm
- Location: Milpitas, CA
- Thanked: 1854 times
- Followed by:523 members
- GMAT Score:770
To determine the coordinates of the midpoint of a line segment, we need to know the coordinates of both the endpoints of the segment. Hence, none od the statements are individually sufficient. Let's check whether together they are sufficient or not.paresh_patil wrote:a & b are positive numbers. What are the co-ordinates of midpoint of segment CD in xy plane?
1) co-ordinates of C are (a,1-b)
2) co-ordinates of D are (1-a,b)
1 & 2 Together: x-coordinate of the midpoint = (x-coordinate of C + x-coordinate of D)/2 = (a + 1 - a)/2 = 1/2
y-coordinate of the midpoint = (y-coordinate of C + y-coordinate of D)/2 = (1 - b + b)/2 = 1/2
Sufficient
The correct answer is C.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT/MBA Expert
- Brent@GMATPrepNow
- 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
Target question: What are the co-ordinates of midpoint of segment CDparesh_patil wrote:a & b are positive numbers. What are the co-ordinates of midpoint of segment CD in xy plane?
1) co-ordinates of C are (a,1-b)
2) co-ordinates of D are (1-a,b)
If we have two points (x1 , y1) and (x2, y2), then the midpoint of this points will be [(x1 + x2)/2 , (y1 + y2)/2]
In other words, to find the midpoint, we find the average of the x-coordinates and the average of the y-coordinates.
Statement 1: co-ordinates of C are (a,1-b)
Since we have no information about point D, there's no way we can find the midpoint of CD.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: co-ordinates of D are (1-a,b)
Since we have no information about point C, there's no way we can find the midpoint of CD.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
We have C(a,1-b) and D(1-a,b), so the midpoint is [(a + 1-a)/2 , (1-b + b)/2]
When we simplify, we get (1/2 , 1/2)
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent