If $P (2, -3)$ and $Q (7, 9)$,then the length of $\overline{PQ}$ is ...........

If $A (4, 7)$ and $B (7, 3),$ then $AB = .............$

State whether the following statement is true or false. Justify your answer.
Points $A(3, 1)$,$B(12, -2)$,and $C(0, 2)$ cannot be the vertices of a 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 $\triangle ABC$.

Find the coordinates of the point on the $X-$axis which is at a distance of $5$ units from $A(4,4)$.

Find the coordinates of the point $R$ on the line segment joining the points $P(-1, 3)$ and $Q(2, 5)$ such that $PR = \frac{3}{5} PQ$.