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Simple Geometry Proof

  1. Jan 7, 2009 #1
    Given 3 points of the triangle:
    (1,2)
    (4,6)
    (9,10)
    Determine if point (5,4) belongs to triangle (is located inside the triangle).

    the only way i can think of doing this is as follows but there must be a more sound way.

    so you have lines:
    (1,2)->(4,6)
    (4,6)->(9,10)
    (1,2)->(9,10)

    you need all 3 of the following to hold true for point (5,4)

    y <= 4/3x + 2/3 (true)
    y >= x + 1 (false)
    y <= 4/5x + 14/5 (false)



    any help greatly appreciated.
     
  2. jcsd
  3. Jan 7, 2009 #2

    symbolipoint

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    If by "Given 3 points" you really mean "Given 3 vertices", then your basic approach is very good. As long as you identified the correct lines, then you can set up the suitable inequalities and determine the necessary truths for the conditions.

    You can easily check about the point by actually drawing the whole graph.
     
    Last edited: Jan 7, 2009
  4. Jan 7, 2009 #3
    Yes I do mean vertices. So this is pretty much the simplest way of going about it?

    Thanks.
     
  5. Jan 7, 2009 #4

    symbolipoint

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    Make the graph of the inequalities; this can help you to explain the proof AND to show the proof graphically. Either the point to test is within the inequalities region or it is not within the inequalities region.
     
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