# Line segments problem with ratios.

1. Nov 4, 2009

### bsodmike

1. The problem statement, all variables and given/known data

The line AB meets the line 3x+2y-21=0 at M. Find the coordinates of M and show that M divides AB in the ratio 2:1

Equation of AB is y=(2/3)x+4

2. Relevant equations

Given solution of M is (3,6).

3. The attempt at a solution

First solve for y such that $y=-\dfrac{3}{2}x+\dfrac{21}{2}$. Was thinking of equating the point-formula to this to find M, of course handling the ratio is an issue. Of course, the line M will have a gradient of m=2/3.

Help in advance is greatly appreciated!

Last edited: Nov 4, 2009
2. Nov 4, 2009

### Staff: Mentor

Are you sure this is the exact wording of the problem? AB would normally be the line segment from point A to point B. If you're not given at least one of the points A or B, I don't know how you're going to show that M divides AB in the specified ratio.

3. Nov 4, 2009

### symbolipoint

The problem description is incomplete. You must be given the coordinates for A and B.

4. Nov 5, 2009

### bsodmike

According to my cousin it is. Her AS level teacher has posed this same question twice.

Hmm that is what I thought as well. Just a thought though, couldn't one use Pythagoras to 'set' A' and B' about M with a ratio 2:1?

Of course, this would result in many answers as not only can one divide the line-segment as 2:1 or 1:2 about M but there is also no restriction on the particular lengths. Frankly, it does seem like an incomplete question as one would expect a singular solution; it is far too arbitrary, especially for AS level!

Thanks Mark and Symbolipoint for your time!