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

Given :

$(-1,6)$ divides the line segment joining the points $(-3,10)$ and B$(6,-8)$.

To find :

We have to find the ratio of division.

Solution :

Let $(-1,6)$ divides $(-3,10)$ and $(6,-8)$ in the ratio $m:n$ internally. 

The section formula is,

$(x, y) = (\frac{m x_{2} + n x_{1}}{m + n} , \frac{m y_{2} + n y_{1}}{m + n})$

Let $P(x, y) = P(-1, 6)$ ; $A (x_{1}, y_{1}) = A(-3, 10)$ ; $B(x_{2}, y_{2}) =  B(6, -8)$

Therefore,

$(-1, 6) = (\frac{m (6) + n(-3)}{m + n} , \frac{m (-8) + n (-3)}{m + n} )$

On comparing,

$-1 = \frac{6m-3n}{m + n}$

$-1(m + n) = 6m-3n$

$-m-n = 6m-3n$

$6m+m-3n+n = 0$

$7m-2n = 0$

$7m = 2n$

$\frac{m}{n} = \frac{2}{7}$

$m : n = 2 : 7$

The required ratio is $2:7$.