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

The points $A(2, 9)$,$B(a, 5)$,and $C(5, 5)$ are the vertices of a triangle $ABC$ right-angled at $B$. Find the value of $a$ and the area of $\triangle ABC$.

$A(k, 2)$ 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 $k$.

The points $(-4,0), (4,0), (0,3)$ are the vertices of a

The coordinates of the point which is equidistant from the three vertices of the $\triangle AOB$ as shown in the figure are

$\overline{AB}$ is given. If $P$ is a point on $\overline{AB}$ such that $P \neq A$ and $P \neq B$,then $P$ divides $\overline{AB}$ from $A$ in the division ratio $\ldots \ldots \ldots \ldots$