Find a point P which divides internally the line segment joining the points A(-3, 9) and B(1, -3) in the ratio 1 : 3.

By section-formula,

Point of division = $\Big(\dfrac{m$1x2 + m2x1}{m1+ m 2}, \dfrac{m1y2 + m2y1}{m1 + m2}\Big)

Given,

m₁ : m₂ = 1 : 3

(x₁, y₁) = (-3, 9)

(x₂, y₂) = (1, -3)

Substituting values we get :

$\Rightarrow P = \Big(\dfrac{1 \times 1 + 3 \times -3}{1 + 3}, \dfrac{1 \times -3 + 3 \times 9}{1 + 3}\Big) \\[1em] \Rightarrow P = \Big(\dfrac{1 - 9}{4}, \dfrac{-3 + 27}{4}\Big) \\[1em] \Rightarrow P = \Big(\dfrac{-8}{4}, \dfrac{24}{4}\Big) \\[1em] \Rightarrow P = (-2, 6).$

Hence, the co-ordinates of P = (-2, 6).