Question

If A, B and C are three points on a line, and B lies between A and C, then $AB+BC=AC$.

• A. True
• B. False

Answer 1

The correct option is A True

Let A, B, and C be three distinct points of a line, with the respective coordinates x, y, and z. If x < y < z, then A-B-C.

Proof, By the ruler postulate:

• AB = |y-x|
• BC = |z-y|
• AC = |z-x|.

But y-x is positive because x < y; similarly, z-y and z-x are positive. So:

• AB = y-x
• BC = z-y
• AC = z-x

Finally:
AB + BC = (y - x) + (z - y)
= z-x
=AC.
Since AB + BC = AC, A-B-C by the definition of between.If A, B and C are three points on a line, and B lies between A and C.