Learn How to Calculate Collinearity of Three Points - Tutorial

Calculate Collinearity of Three Points - Definition, Formula and Example

Definition:

Collinearity occurs in a plane, if three or more points lie on the same straight line. Three points namely, A(x1, y1), B(x2, y2) and C(x3, y3) are considered as collinear, when any one of these points is positioned at the straight line that joins the rest of the points.

Formula:

Area = 1/2{ (x1 y2 + x2 y3 + x3 y1) - ( x2 y1 + x3 y2 + x1 y3) } If the resultant value is equal to zero, then the points are collinear. If the resultant value is not equal to zero, then the points are non-collinear.
Example:

Consider that there exists three points in a plane namely, x1, x2, x3 and y1, y2, y3. Assume the values for the points as x1=1, x2=3, x3=4, and y1=2, y2=2, y3 =5. Compute the co linearity for the given three points?

Given,

x1=1, x2=3, x3=4, y1=2, y2=2, y3 =5

To find,

Collinearity of x1 y1, x2 y2, x3 y3

Solution:

Let us calculate the co linearity between the points x1y1, x2y2, x3y3. Substitute the values in the area formula,

Area= 1/2 { (x1 y2 + x2 y3 + x3 y1) - ( x2 y1 + x3 y2 + x1 y3) }
 = 1/2 { (2 + 15 + 8) - (6 + 8 + 5) }
 = 1/2 (25 - 19)
 =1/2 (6)
 =3

The result 3 is not equal to zero. Therefore, the given points are non-collinear.

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