Line segments problem with ratios.

[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!

[Mark44]

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

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.


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!

[symbolipoint]

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

[bsodmike]

Are you sure this is the exact wording of the problem?

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

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.

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!