P and Q are the points (−4,3) and (2,1) respectively.

Question

What are the coordinates of the point M which divides QP externally in the ratio 4:5?

Answer 1

The coordinates are P(- 4, 3) and Q(2, 1)

Formula for the external dividing point of P and Q in the ratio of m₁ : m₂

M(x, y) = [(m₁x₂ - m₂x₁)/(m₁- m₂), (m₁y₂ - m₂y₁)/(m₁- m₂) ]

The ratio 4 : 5 = m₁ : m₂

(- 4, 3) = (x₁, y₁) and (2, 1) = (x₂, y₂)

M(x, y)  = { [(4(2) - 5(- 4)]/(4 - 5), [4(1) - 5(3)]/(4 - 5) }

= [ (8 + 20)/(- 1) , (4 - 15)/(- 1) ]

M = (- 28, 11).