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Line segments problem with ratios.

  1. Nov 4, 2009 #1
    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 [itex]y=-\dfrac{3}{2}x+\dfrac{21}{2}[/itex]. 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. jcsd
  3. Nov 4, 2009 #2

    Mark44

    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.
     
  4. Nov 4, 2009 #3

    symbolipoint

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    Homework Helper
    Education Advisor
    Gold Member

    The problem description is incomplete. You must be given the coordinates for A and B.
     
  5. Nov 5, 2009 #4
    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!
     
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