1. Sep 21, 2008

### mathstudent88

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.