Q5 of 256 Page 7

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

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

⇒

If the points (a, 0), (o, b) and (1, 1) are collinear, prove that a + b = ab.

Using determinants prove that the points (a, b) (a’, b’) and (a – a’, b – b’) are collinear if ab’ = a’b.

Find the value of x if the area of a triangle is 35 square cms with vertices (x, 4), (2, – 6) and (5, 4).

Using determinants, find the area of a triangle whose vertices are (1, 4), (2, 3) and (– 5, – 3). Are the given points collinear?