What is the formula of Collinearity of Three Points

Here are some common ways to prove that three points are collinear

Method 1

Find the area of triangle formed by the three points.

If the area is zero(0) , three points are collinear. If (x1,y1), (x2,y2) & (x3, y3) using the following formula

Area =1/2{x1(y2-y3)+x2(y3-y1)+x3(y1-y2)}

Method 2

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.

if:

(i) AB + BC = AC Or,

(ii) AB + AC = BC Or,

(iii) AC + BC = AB