The formula of the area of a triangle can be used to prove that three points $A(x_1,y_1), B(x_2,y_2)$ and $C(x_3,y_3)$ are collinear.

If the area of the triangle formed by these three points is zero(0), then the points are collinear.

Area of a triangle $=\frac{1}{2}\left|x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right|$