Find the circumcentre of $\Delta ABC$ with vertices $A(-1, 1)$,$B(0, -4)$,and $C(-1, -5)$.

Find the ratio in which the point $P \left(\frac{3}{4}, \frac{5}{12}\right)$ divides the line segment joining the points $A \left(\frac{1}{2}, \frac{3}{2}\right)$ and $B(2, -5)$. (in $: 5$)

If $A(4, 3)$ and $B(8, 9)$,then the midpoint of $\overline{AB}$ is $\ldots \ldots \ldots \ldots .$

$A(k, 2)$ and $B(3, 5)$ are the given points. If the point $P(t, t)$ divides the line segment $\overline{AB}$ in the ratio $k:1$ starting from $A$,find the value of $k$.

$A(6,1), B(8,2)$ and $C(9,4)$ are three vertices of a parallelogram $ABCD$. If $E$ is the midpoint of $DC$,find the area of $\triangle ADE$ (in sq. units).

The fourth vertex $D$ of a parallelogram $ABCD$ whose three vertices are $A(-2,3)$,$B(6,7)$,and $C(8,3)$ is