If the points A(-

Given points A(-2, 1), B(a, b) and C(4, -1) are collinear

And a – b = 1 …(1)

We have to find the values of a and b.

Since the given points are collinear, the area of the triangle formed by them must be 0.

We know that the area of Triangle =

⇒ [x₁(y₂ – y₃) + x₂(y₃ – y₁) + x₃(y₁ – y₂)] = 0

⇒ [-2(b – (-1)) + a(-1 – 1) + 4(1 – b)] = 0

⇒ [-2(b + 1) -2a + 4(1 – b)] = 0

⇒ [-2b -2 -2a + 4 – 4b] = 0

⇒ -2a - 6b + 2 = 0

⇒ -2a – 6b = -2

Dividing by -2, we get

⇒ a + 3b = 1

⇒ a = 1- 3b … (2)

Substituting (2) in (1),

⇒ (1 – 3b) – b = 1

⇒ 1 – 4b = 1

⇒ 4b = 0

∴ b = 0

Substituting value of b in (1),

⇒ a - 0 = 1

∴ a = 1

Ans. The values of a and b are 1 and 0 respectively.