Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).

Let ratio be k : 1.

By section-formula,

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

Substituting values we get :

$\Rightarrow (-1, 6) = \Big(\dfrac{k \times 6 + 1 \times -3}{k + 1}, \dfrac{k \times -8 + 1 \times 10}{k + 1}\Big) \\[1em] \Rightarrow (-1, 6) = \Big(\dfrac{6k - 3}{k + 1}, \dfrac{-8k + 10}{k + 1}\Big) \\[1em] \Rightarrow -1 = \dfrac{6k - 3}{k + 1} \text{ and } 6 = \dfrac{-8k + 10}{k + 1} \\[1em] \Rightarrow -k - 1 = 6k - 3 \text{ and } 6k + 6 = -8k + 10 \\[1em] \Rightarrow 6k + k = -1 + 3 \text{ and } 6k + 8k = 10 - 6 \\[1em] \Rightarrow 7k = 2 \text{ and } 14k = 4 \\[1em] \Rightarrow k = \dfrac{2}{7} \text{ and } k = \dfrac{4}{14} = \dfrac{2}{7}.$

∴ k : 1 = $\dfrac{2}{7} : 1$ = 2 : 7.

Hence, ratio = 2 : 7.