If the points A(x,2), B(-3,-4) and C(7,-5) are collinear, then find the value of x.

Given points A(x, 2), B(-3, -4) and C(7, -5) are collinear.

We have to find the value of x.

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

We know that the area of Triangle = .

∴ = 0

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

⇒ [x(-4 – (-5)) + (-3)(-5 – 2) + 7(2 – (-4))] = 0

⇒ [x + 21 + 42] = 0

⇒ x + 63 = 0

⇒ x = -63

Ans. The value of x is -63.