BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Coordinate geometry - intersection points?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 85
Joined: Tue Sep 02, 2008 12:13 am
Thanked: 1 times
GMAT Score:650

Coordinate geometry - intersection points?

by vzzai » Tue Nov 15, 2011 12:50 am
I know that if 2 equations are given we could find the intersection by solving the equations.
But, what if an intersection point (equation) is given, and asked to find out if this is an intersection of 2 lines?
1) gives one of the equations

Is that enough information to solve?

I'm sorry, if the question sounds vague but I'm curious to know the method.
Thank you,
Vj
Top
Source: — Data Sufficiency |
User avatar
Community Manager
Posts: 1060
Joined: Fri May 13, 2011 6:46 am
Location: Utrecht, The Netherlands
Thanked: 318 times
Followed by:52 members

by neelgandham » Tue Nov 15, 2011 1:28 am
If a*x + b*y = c and a1*x + b1*y = c1 are the equations of the two lines and the intersection point of these lines is (b,d), then the point should satisfy both the line equations. i.e. a*b + b*d should be equal to c and a1*b + b1*d should be equal to c1. Only if both the conditions are satisfied, one can tell that the point is the intersection point !

Hope that answers your question!
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/
Top

GMAT/MBA Expert

User avatar
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

by Anurag@Gurome » Tue Nov 15, 2011 2:49 am
vzzai wrote:I know that if 2 equations are given we could find the intersection by solving the equations.
But, what if an intersection point (equation) is given, and asked to find out if this is an intersection of 2 lines?
1) gives one of the equations

Is that enough information to solve?

I'm sorry, if the question sounds vague but I'm curious to know the method.
What can be understood from your query is that if the equation of one of the lines is given say
ax + by = c, then we need to determine whether(p,q) is a point of intersection of this line and one more line.
Firstly this point (p,q) should lie on the line ax + by = c.
This means that ap + bq = c should be true.
Then, obviously, (p, q) can be the point of intersection of the line ax + by = c and any other line that passes through this point.
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/
Top
Senior | Next Rank: 100 Posts
Posts: 85
Joined: Tue Sep 02, 2008 12:13 am
Thanked: 1 times
GMAT Score:650

by vzzai » Tue Nov 15, 2011 6:00 am
Thank you Anurag. Your explanation clarifies my vague question. :)
Thank you,
Vj
Top
Master | Next Rank: 500 Posts
Posts: 268
Joined: Mon Mar 15, 2010 12:10 am
Thanked: 13 times

by shekhar.kataria » Wed Nov 23, 2011 11:33 am
Anurag@Gurome wrote:
vzzai wrote:I know that if 2 equations are given we could find the intersection by solving the equations.
But, what if an intersection point (equation) is given, and asked to find out if this is an intersection of 2 lines?
1) gives one of the equations

Is that enough information to solve?

I'm sorry, if the question sounds vague but I'm curious to know the method.
What can be understood from your query is that if the equation of one of the lines is given say
ax + by = c, then we need to determine whether(p,q) is a point of intersection of this line and one more line.
Firstly this point (p,q) should lie on the line ax + by = c.
This means that ap + bq = c should be true.
Then, obviously, (p, q) can be the point of intersection of the line ax + by = c and any other line that passes through this point.
HI Anurag

I am little confused between ur explanation and the Question asked.

I understand your explanation above but the Question says that you know the intersection point and the equation of the one line and we need to know whether this point is an intersection point of the two line. Now this may be a interaction point as u proved above but the second line may not pass through this point.

I am not sure may be i am not righly interpretting the Question. Please clerify.

Thanks in advance.
Restlessness and discontent are the first necessities of progress.--Thomas A. Edison

If you find this post helpful, let me know by clicking thanks above :-)
Top
Post new topic Post Reply
• Page 1 of 1