Question

By using section formula show that the points (1,1),(3,-2) and(-1,4) are collinear.

Answer 1

Let point B(1,1) divides the line segment joining the points A(-1,4) and

C(3,-2) in the ratio k:1

Applying these in Section Formula

B(x,y) = (m₂x₁ + m₁x₂ / m₁ + m₂) , (m₂y₁ + m₁y₂ / m₁ + m₂)

Taking x co-ordinate,

Then,

1 = 1(-1) + k(3) / k + 1

k + 1 = 3k - 1

2k = 2  ⇒ k =1

Now, Taking y co-ordinate

1 = 1(4) + k(-2) / k + 1

k + 1 = 4 - 2k

3k = 3   ⇒ k = 1

As Ratio at both x and y co-ordinates are k:1 → 1:1. 

This  implies that B is the mid point of AC line.

Hence These points are collinear.
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