co-ordinate geometry .

This topic has expert replies
User avatar
Senior | Next Rank: 100 Posts
Posts: 32
Joined: 16 Jul 2011

co-ordinate geometry .

by Md.Nazrul Islam » Sat Mar 31, 2012 5:09 pm
In a co-ordinate system ,if three points (5,3) (x,4)and (3,2)lie on the same line ,what is the value of the x ?

User avatar
GMAT Instructor
Posts: 1248
Joined: 29 Mar 2012
Location: Everywhere
Thanked: 503 times
Followed by:191 members
GMAT Score:780

by [email protected] » Sat Mar 31, 2012 5:17 pm
We can use the two known points to find the slope of the line:

=(y2 - y1)/(x2 - x1)
=(3 - 2)/(5 - 3)

In other words, we move up 1 unit for every 2 units we move right.

Since (x,4) is one unit up from (5, 3), x must be 2 units to the right of 5, which gives us a value of 7.
Join Veritas Prep's 2010 Instructor of the Year, Matt Douglas for GMATT Mondays

Visit the Veritas Prep Blog

Try the FREE Veritas Prep Practice Test

User avatar
Junior | Next Rank: 30 Posts
Posts: 15
Joined: 26 Mar 2012
Thanked: 3 times

by gmatmath » Fri Apr 06, 2012 8:34 am
if (5,3), (x,4) and (3,2) lie on the same line, they are collinear.
This means that the slope of any 2 points taken should be the same.

1)(5,3) and (x,4)
slope = (4-3)/(x-5)

2) (5,3) and (3,2)
slope = (2-3)/(3-5)

Now, equating both the slopes

1/(x-5) = -1/-2
==> 1/(x-5) = 1/2
since the numerators are equal, we can equate the denominators.

So, x-5 = 2
==> x = 7

User avatar
Community Manager
Posts: 1060
Joined: 13 May 2011
Location: Utrecht, The Netherlands
Thanked: 318 times
Followed by:52 members

by neelgandham » Fri Apr 06, 2012 9:46 am
As mentioned by Bill and gmatmath, Slope formula works best.

But here is something I do,
if I have no clue,
how to do
- ah it rhymes!
(Not only to solve this problem, but to solve any geometry problem). We all know that the erase pad provided in the GMAT exam centre contains grids. So, I use the grid lines to draw a Cartesian coordinate system and plot the points in the system. For example, in the question above, I plotted the points (5,3) and (3,2). I, then extended the line segment to meet the line y = 4 at (7,4). and the rest...

p.s: Use this as the last resort[/i}
The attachment is self-explanatory.
BeattheGMAT - Erase Board.JPG
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at