Question

Using the determinants prove that the points (a, b), (a’, b’) and (a – a’, b – b) are collinear if a b’ = a’ b.

Answer 1

The points (a, b), (a’, b’) and (a – a’, b – b) are collinear

The condition given that three points to be collinear, the area of the triangle formed by these points will be zero. As we know that, vertices of a triangle are (x₁, y₁), (x₂, y₂) and (x₃, y₃), then the area of the triangle is given by,

On expanding along R₁ 

Hence proved.