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!!