Find the value of λ so that the points (1, – 5), (– 4, 5) and (λ, 7) are collinear.

Question

Find the value of λ so that the points (1, – 5), (– 4, 5) and ( λ , 7) are collinear.

Philoid · Accepted Answer

Given: – (1, – 5), (– 4, 5) and (λ, 7) are collinear

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

⇒

⇒ 50 – 10λ = 0

⇒ λ = – 5

⇒