If the lines p1x + q1y = 1, p2x + q2y = 1 and p3x + q3y = 1 be concurrent, show that the points (p1, q1), (p2, q2) and (p3, q3) are collinear.

Given:

   

   

and ,

   

The given lines can be written as follows:

   

   

and,

   

since, the three lines are concurrent.

Now, consider the following determinant:

Hence proved, the given three points,

(p₁, q₁), (p₂, q₂) and (p₃, q₃) are collinear.