Question

By using the concept of equation of a line, prove that the three points (3, 0), (- 2, – 2) and (8, 2) are collinear.

Answer 1

Let A(3, 0), B(- 2, 2) and C(8, 2) be the given points Using two-point form, we can find the equation of AB as

y - 0 = (- 2 - 0)/(- 2 - 3)(x - 3)

⇒ y = 2/5(x - 3)

⇒ 5y = 2x - 6 ....(1)

If C(8, 2) lies on the line (1) then we can conclude A, B and C are collinear. 

Now putting x = 8 and y =2 in (1), we get 

5(2) = 2(8) – 6 

10 = 16 – 6= 10 

10 – 10 = 0 

= Clieson(1) 

= A, B and C are collinear