Question

The three points are A (-1,3), B (2,1) and C (5,-1). Show that |AB|+|BC|=|AC| ​

Answer 1

Answer:

We will discuss here how to prove the conditions of collinearity of three points.

Collinear points: Three points A, B and C are said to be collinear if they lie on the same straight line.

There points A, B and C will be collinear if AB + BC = AC as is clear from the adjoining figure.

In general, three points A, B and C are collinear if the sum of the lengths of any two line segments among AB, BC and CA is equal to the length of the remaining line segment, that is,

either AB + BC = AC or AC +CB = AB or BA + AC = BC.

In other words,

There points A, B and C are collinear iff:

(i) AB + BC = AC i.e.,

Or, (ii) AB + AC = BC i.e. ,