Find the ratio in which the point P( −1, y), lying on the line segment joining points A(−3, 10) and B(6, −8) divides it.

Let k be the ratio in which P( −1, y) divides the line segment joining the points A(−3, 10) and B(6, −8). Then

$(-1, y)=\left(\frac{k(6)-3}{k+1}, \frac{k(-8)+10}{k+1}\right)$

$\Rightarrow \frac{k(6)-3}{k+1}=-1$ and $y=\frac{k(-8)+10}{k+1}$

$\Rightarrow k=\frac{2}{7}$

Substituting $k=\frac{2}{7}$ in $y=\frac{k(-8)+10}{k+1}$, we get

$y=\frac{\frac{-8 \times 2}{7}+10}{\frac{2}{7}+1}=\frac{-16+70}{9}=6$

Hence, the required ratio is 2 : 7 and y = 6.