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Geometry help please!

  1. Sep 21, 2008 #1
    Prove:
    Given a line L with a coordinate system f, and three points A,B, and C with coordinates x, y, and z respectively. If A-B-C, then x-y-z.



    I was thinking that I could do it this way, but I'm not quite sure.

    If A<B<C, then

    xy=|B-A|=B-A

    because B-A>0.

    Then,

    yz=|C-B|=C-B
    and

    xz=|C-A|=C-A.

    Therefore

    xy+yz=(B-A)+(C-B)
    = C-A
    =|C-A|
    = xz

    so x-y-z.

    If C<B<A, it follows precisely similar argument that z-y-x, which means that x-y-z as before.

    Is this right? If not could you please help me?

    Thank you!!
     
  2. jcsd
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