By using the concept of equation of a line, prove that the three points (3, 0), (– 2, – 2) and (8, 2) are collinear.

If we have to show that the given three points (3, 0), (– 2, – 2) and (8, 2) are collinear, we have to show that the line passing through the points (3, 0) and (– 2, – 2) also passes through the point (8, 2).

We know that the equation of the line passing through the points (x₁, y₁) and (x₂, y₂) is given by

∴

⇒

⇒ -5y = -2 (x – 3)

⇒ -5y = -2x + 6

⇒ 2x – 5y = 6

If 2x – 5y = 6 passes through (8, 2),

LHS = 2x – 5y = 2(8) – 5(2) = 16 – 10 = 6 = RHS

The line passing through the points (3, 0) and (– 2, – 2) also passes through the point (8, 2).

Hence proved.

Ans. The given three points are collinear.