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

If the centroid of the triangle with vertices $(-5, 3), (a, -1), (6, b)$ is $(1, -1)$,then find the values of $a$ and $b$.

State whether the following statement is true or false. Justify your answer.
The point $A (2,7)$ lies on the perpendicular bisector of the line segment joining the points $P (6,5)$ and $Q (0,-4)$.

For $A(0, 0)$ and $B(4, 8)$,$M$ is the midpoint of $\overline{AB}$ and $N$ is the midpoint of $\overline{BM}$,then the coordinates of $N$ are.........

If the vertices of $\Delta ABC$ are $A(x_{1}, y_{1})$,$B(x_{2}, y_{2})$,and $C(x_{3}, y_{3})$,then the centroid of $\Delta ABC$ is........

The perpendicular bisector of the line segment joining the points $A(1, 5)$ and $B(4, 6)$ cuts the $y$-axis at