Show that the points (a + 5, a – 4), (a – 2, a + 3) and (a, a) do not lie on a straight line for any value of a.

Given points are (a + 5, a – 4), (a – 2, a + 3) and (a, a)

To Prove: these points don’t lie on straight line for any value of a

So, we have to show that these points form a triangle.

Area of triangle:-

Applying R₂→ R₂ – R₁, we get

Applying R₃→ R₃ – R₁, we get

Now, expanding along third column, we get

Hence, given points form a triangle i.e. points do not lie on a straight line.

Hence Proved