If $A (5, 3)$ and $B (3, 3)$,then the midpoint of $\overline{AB}$ is $\ldots \ldots \ldots .$

State whether the following statement is true or false. Justify your answer.
$A$ circle has its centre at the origin and a point $P(5,0)$ lies on it. The point $Q(6,8)$ lies outside the circle.

Show that $(10, -18), (3, 6)$ and $(-5, 2)$ are the vertices of an isosceles triangle.

Prove that the points $A(1, -2)$,$B(2, 3)$,$C(-3, 2)$,and $D(-4, -3)$ are the vertices of a rhombus.

If $(-4,3)$ and $(4,3)$ are two vertices of an equilateral triangle,find the coordinates of the third vertex,given that the origin lies in the interior of the triangle.

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 $\triangle ABC$.