If three points are on the same line, then they are collinear. points x, y, and z are on line m.

Condition for collinearity of three points on a line.      

Step-by-step explanation:

We are given the following information in the question:

Point X, Y and Z lies on a line m.

We have to show that these points are collinear. Three points on a point are collinear if the area of triangle formed by these three points is zero.

We make the following assumptions.

Let be the coordinates of point X, Y and Z respectively.

Then the area of triangle formed by these three points is given by:

Equating area of triangle to zero,

Hence, the above condition is the condition foe collinearity of three points on a given line.