Find the ratio in which the point (– 3, k) divides the join of A(– 5, – 4) and B(– 2, 3). Also, find the value of k. [CBSE 2007]

Question

Philoid · Accepted Answer

– 3 = (m₁x₂ + m₂x₁)/ m₁ + m₂

– 3 = (m₁ × (– 2) + m₂ (– 5))/ m₁ + m₂

– 3 = (– 2m₁ – 5m₂ ) / m₁ + m₂

– 2m₁ – 5m₂ = – 3(m₁ + m₂ )

2m₁ + 5m₂ = 3(m₁ + m₂ )

m₁ – 2m₂ = 0

m₁:m₂ = 1:2

Now,

K = (m₁y₂ + m₂y₁)/ m₁ + m₂

K = (m₁ × 3 + m₂(– 4))/ m₁ + m₂

K = (3m₁ – 4m₂ ) / m₁ + m₂

3m₁ – 4m₂ = k(m₁ + m₂)

Putting the values of m₁ & m₂

k = 2/3

Hence,2:1, k = 2/3