coordinate geometry .
This topic has expert replies
 Md.Nazrul Islam
 Senior  Next Rank: 100 Posts
 Posts: 32
 Joined: 16 Jul 2011
In a coordinate system ,if three points (5,3) (x,4)and (3,2)lie on the same line ,what is the value of the x ?
 [email protected]
 GMAT Instructor
 Posts: 1248
 Joined: 29 Mar 2012
 Location: Everywhere
 Thanked: 503 times
 Followed by:191 members
 GMAT Score:780
We can use the two known points to find the slope of the line:
=(y2  y1)/(x2  x1)
=(3  2)/(5  3)
=1/2
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.
=(y2  y1)/(x2  x1)
=(3  2)/(5  3)
=1/2
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
Visit the Veritas Prep Blog
Try the FREE Veritas Prep Practice Test
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 = (43)/(x5)
2) (5,3) and (3,2)
slope = (23)/(35)
Now, equating both the slopes
1/(x5) = 1/2
==> 1/(x5) = 1/2
since the numerators are equal, we can equate the denominators.
So, x5 = 2
==> x = 7
This means that the slope of any 2 points taken should be the same.
1)(5,3) and (x,4)
slope = (43)/(x5)
2) (5,3) and (3,2)
slope = (23)/(35)
Now, equating both the slopes
1/(x5) = 1/2
==> 1/(x5) = 1/2
since the numerators are equal, we can equate the denominators.
So, x5 = 2
==> x = 7
 neelgandham
 Community Manager
 Posts: 1060
 Joined: 13 May 2011
 Location: Utrecht, The Netherlands
 Thanked: 318 times
 Followed by:52 members
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 selfexplanatory.
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 selfexplanatory.
 Attachments

Anil Gandham
Welcome to BEATtheGMAT  Photography  Getting Started  BTG Community rules  MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
Welcome to BEATtheGMAT  Photography  Getting Started  BTG Community rules  MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/