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External division of a line segment

  1. May 8, 2013 #1
    Suppose AB is a straight line segment. To divide the segment externally at point C in the ratio m:n, is it necessary for C to remain always outside of AB? I always thought C should be outside of AB, but the post in the link below confuses me
    http://www.transtutors.com/math-homework-help/vectors/section-formula.aspx
    Basically what is meant by external division of line segment by a point?
    Can anyone please clarify me? Thanks.
     
  2. jcsd
  3. May 8, 2013 #2

    SteamKing

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    I'm not sure what you are asking. In the link, the point C is clearly on the line segment between A and B.
    The point O is external to the line segment.
     
  4. May 8, 2013 #3

    haruspex

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    I would guess it means that the distances AC, BC should be in the ratio m:n. If that represents AC:BC (as opposed to the other way around) then there are two solutions, one internal and one external.
     
  5. May 12, 2013 #4
    uploadfromtaptalk1368360807272.jpg
    Thanks for your response.
    I'm trying to know if C is on line segment between A and B (fig 2) then can it divide AB externally or not? In the link it says C divides AB externally in the ratio AC:AB =m:n, is it correct or not?

    Sorry for not stating clearly.


    In (fig 1) if C divides AB externally then which pair of segments should we consider AC:CB or AC :AB?
    Or does this consideration of segments depend on given ratios? (for m+n:n, AC:CB for m+n:m, AC:AB)
     
    Last edited: May 12, 2013
  6. May 12, 2013 #5

    haruspex

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    In the construct "C divides AB", A and B have symmetric roles, whereas C is different. Therefore it's AC:CB.
     
  7. May 13, 2013 #6
    What have you meant by "A and B have symmetric roles" here?
    Please explain a little more. And what about the second fig, that if C is in between A and B on AB, then can it divide AB externally?
    Sorry for bothering you. :confused:
     
  8. May 13, 2013 #7

    haruspex

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    "C divides AB" is the same statement as "C divides BA". The roles that B and A play in the statement are symmetric, so the two are interchangeable. In the ratio expression AC:AB, B and A are not interchangeable; AC:AB is different from BC:BA. Therefore the correct interpretation is the ratio AC:BC.
    If you compare the vertex labels A, B and C with the vector labels a, b, c you will see that there's an error in the diagram.
     
  9. May 13, 2013 #8
    Thanks a lot haruspex :)
     
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