## co-ordinate geometry.

##### This topic has expert replies

- Md.Nazrul Islam
- Senior | Next Rank: 100 Posts
**Posts:**32**Joined:**16 Jul 2011

For 3 points to be collinear, the slope of 2 points taken at a time will be equal.

A(5,3), B(x,y), C(3,2)

slope for 2 points(x1,y1) and (x2,y2) is given by (y2-y1)/(x2-x1)

**Slope m1 = (y-3)/(x-5)**

slope m2 = (2-y)/(3-x)

slope m2 = (2-y)/(3-x)

m1 = m2 as they lie on the same line.

(y-3)/(x-5) = (2-y)/(3-x)

==> (y-3)(3-x) = (2-y)(x-5)

==> 3y - 9 -xy +3x = 2x - 10 - xy + 5y

==>

**x + 1 = 2y-------(eqn 1)**

slope of AC = m3 = (2-3)/(3-5)

m3 = -1/-2

**m3 = 1/2**

**from eqn 1, x = 2y - 1**

giving values for y, we can get values for x.

y = 0, x = -1

y = 1, x = 1

y = 2, x = 3

giving values for y, we can get values for x.

y = 0, x = -1

y = 1, x = 1

y = 2, x = 3

and so on...

- Shalabh's Quants
- Master | Next Rank: 500 Posts
**Posts:**134**Joined:**06 Apr 2012**Thanked**: 35 times**Followed by:**5 members

All 3 points lie in St. Line. So it will have infinite set of solutions for x & y.Md.Nazrul Islam wrote:In a co-ordinate system , if three points (5,3)(x,y) and (3,2)lie on a same line ,fine the value of X.

Lets find out Eqn of St. Line...

y-y'=[(y"-y')/(x"-x")]*(x-x')

=> y-3=[(2-3)/(3-5)]*(x-5)

.

.

.

=> It reduces to x=2y+1;

As it is a linear eqn with 2 variables, hence it will have infinite solutions.

=> This eqn. will seek any value of x & yield corresponding infinite values of y.

Shalabh Jain,

e-GMAT Instructor

e-GMAT Instructor

### GMAT/MBA Expert

- [email protected]
- GMAT Instructor
**Posts:**3835**Joined:**02 Apr 2010**Location:**Milpitas, CA**Thanked**: 1854 times**Followed by:**523 members**GMAT Score:**770

Md.Nazrul Islam wrote:In a co-ordinate system , if three points (5,3)(x,y) and (3,2)lie on a same line ,fine the value of X.

**Since the three points lie on the same line, so the slope of any two points will be the same.**

Now slope of a line passing through (x1, y1) and (x2, y2) = (y2 - y1)/(x2 - x1)

Slope of line passing through (5, 3) and (x , y) = (y - 3)/(x - 5)

Slope of line passing through (x, y) and (3 , 2) = (2 - y)/(3 - x)

Now, Slope of line passing through (5, 3) and (x , y) = Slope of line passing through (x, y) and (3 , 2)

(y - 3)/(x - 5) = (2 - y)/(3 - x)

(y - 3)(3 - x) = (2 - y)(x - 5)

3y - 9 - xy + 3x = 2x - xy - 10 + 5y

x - 2y = -1 ... Equation 1

Similarly, slope of line through (5, 3) and (3, 2) = Slope of line passing through (x, y) and (3 , 2)

(2 - 3)/(3 - 5) = (2 - y)/(3 - x)

(-1/-2) = (2 - y)/(3 - x)

1/2 = (2 - y)/(3 - x)

3 - x = 2(2 - y)

3 - x = 4 - 2y

x - 2y = -1 ... Equation 2

Both equations 1 and 2, give the same equation, so we can have infinite solutions to this, and hence infinite values for x.

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/