The mid-point of the line segment joining the points $A(-2, 8)$ and $B(-6, -4)$ is

For the triangle with vertices $A (6, 7),$ $B (-2, 3)$ and $C (9, 1),$ find the coordinates of the point on $\overline{BC}$ where the bisector of $\angle A$ intersects $\overline{BC}$.

Find the points of trisection of the line segment joining $(-2,-1)$ and $(7,8)$.

In which ratio does the $Y-$axis divide the line segment joining $A (-4, 1)$ and $B (1, 1)$ from $A$ (in $:1$)?

In what ratio does the $x$-axis divide the line segment joining the points $(-4, -6)$ and $(-1, 7)$? Find the coordinates of the point of division.

The line segment joining the points $A(3, 2)$ and $B(5, 1)$ is divided at the point $P$ in the ratio $1: 2$,and it lies on the line $3x - 18y + k = 0$. Find the value of $k$.