Can someone help me with these relations? I don't understand them...?

Question

Points A, B, C are on a line in the order ABC. What can be said about the distance AC in relation to the distance AB, BC?
AB - AC = BC
AB + BC = AC
AC + BC = AB


A, B, C are points with B in the line AC. What can be said about the distance AC in relation to the distances AB, BC?
AB + BC = AC
AB - AC = BC
AC + BC = AB

I don't understand how you find the answer to these. Can you please explain? Thanks in advance!

Answer 1

The key fact is that they are ON A LINE.

Because of that, AB + BC = AC.

If they weren't on a line, then it would be the case that AB + BC > AC.

For the second one, you don't have the order of the points. The first of the three cases is correct if B is between A and C. The second is correct if C is between A and B. The third is the same thing as the second.