Find the co-ordinates of point P which divides the line segment joining A(-2, -7) and B(6, 1) in the ratio 5 : 3.

Let point P be (x, y).

Given,

m₁ : m₂ = 5 : 3

By section-formula,

(x, y) = $\Big(\dfrac{m$1x2 + m2x1}{m1 + m2}, \dfrac{m1y2 + m2y1}{m1 + m2}\Big)

Substituting values we get :

$\Rightarrow (x, y) = \Big(\dfrac{5 \times 6 + 3 \times -2}{5 + 3}, \dfrac{5 \times 1 + 3 \times -7}{5 + 3}\Big) \\[1em] \Rightarrow (x, y) = \Big(\dfrac{30 - 6}{8}, \dfrac{5 - 21}{8}\Big) \\[1em] \Rightarrow (x, y) = \Big(\dfrac{24}{8}, \dfrac{-16}{8}\Big) \\[1em] \Rightarrow (x, y) = (3, -2).$

Hence, the coordinates of P are (3, -2).