# Calculate Collinearity of Three Points

Calculate Collinearity for given 3-points A, B, C and tells points are collinear or non-collinear.

### Formula used

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

### Methods to Prove if Points are Collinear

There are following methods to find whether the three points are collinear or not collinear:

#### Slope Formula Method

If the slope of any two pairs of points is the same than three points are collinear. As shown in fig. with three points A, B and C, three pairs of points can be formed, they are: AB, BC and AC. If Slope of BC = slope of BC = slope of AC, then A, B and C are collinear points.

#### Area of Triangle Method

Three points are collinear if the value of the area of the triangle formed by the three points is equal to zero, means If the result for the area of the triangle is zero, then the given points are collinear.

#### Example of non-collinear

Lets find the collinearty for three points (3, 2), (33, 44) and (4, 3)

Area = 1/2{ (x1 y2 + x2 y3 + x3 y1) - ( x2 y1 + x3 y2 + x1 y3) } = 1/2{(132+99+8) - (66+176+9 )} = 1/2(239 - 251) = 1/2(-12) = -6 Area != 0; The given points are non collinear

#### Example of collinear

Lets find the collinearty for three points (3, 2), (5, 4) and (7, 6)

Area = 1/2{ (x1 y2 + x2 y3 + x3 y1) - ( x2 y1 + x3 y2 + x1 y3) } = 1/2{(12+30+14) - (10+28+18 )} = 1/2(56 - 56) = 1/2(0) = 0 Area = 0; The given points are collinear