The circumcentre of the triangle with vertices $(6,0), (0,0)$ and $(0,8)$ is $\ldots \ldots \ldots$

If the circumcentre of the triangle with vertices $(a, -1)$,$(6, -9)$,and $(10, b)$ is $(6, -5)$,then find the values of $a$ and $b$.

If $D\left(\frac{-1}{2}, \frac{5}{2}\right)$,$E(7, 3)$,and $F\left(\frac{7}{2}, \frac{7}{2}\right)$ are the midpoints of the sides of $\triangle ABC$,find the area of $\triangle ABC$.

$A$ line intersects the $y$-axis and $x$-axis at the points $P$ and $Q$,respectively. If $(2, -5)$ is the mid-point of $PQ$,then the coordinates of $P$ and $Q$ are,respectively:

If the midpoint of a line segment joining $(3, 4)$ and $(a, 8)$ is $(4, 6)$,then $a = \ldots$

State whether the following statement is true or false. Justify your answer.
Point $P (0, -7)$ is the point of intersection of the $y$-axis and the perpendicular bisector of the line segment joining the points $A (-1, 0)$ and $B (7, -6)$.