If the points (3, – 2), (x,2) and (8,8) are collinear, find x using determinant.

Given: – (3, – 2), (x,2) and (8,8) are collinear points

Tip: – For Three points to be collinear, the area of the triangle formed by these points will be zero

Now, we know that,

Vertices of a triangle are (x₁,y₁), (x₂,y₂) and (x₃,y₃), then the area of the triangle is given by:

Now,

Substituting given value in above formula

⇒

Expanding along R₁

⇒

⇒ [x(– 6) + 2(x – 8) + 1(8x – 16)] = 0

⇒ – 6x + 2x – 16 + 8x – 16 = 0

⇒ 10x = 50

⇒ x = 5