Q3 of 256 Page 7

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

Given: – (a, 0), (o, b) and (1, 1) are collinear points

To Prove: – a + b = ab

Proof: –

Tip: – If Three points to be collinear, then 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:

Thus

Expanding along R₁

⇒

⇒ a + b = ab

Hence Proved

Using determinants show that the following points are collinear:

(3, – 2), (8, 8) and (5, 2)

Using determinants show that the following points are collinear:

(2, 3), (– 1, – 2) and (5, 8)

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