Question

If the points A, B and C lie on the same line then write the relation between AB, BC and AC.

Answer 1

ANSWER

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.