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

The midpoint of the line segment joining $(1, 1)$ and $(3, 3)$ is:

The coordinates of the midpoint of the line segment joining $(8, 10)$ and $(4, 8)$ are ..............

The coordinates of the midpoint of a line segment joining $A (3, -2)$ and $B (-1, 4)$ are:

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 $\triangle ABC$.

The points $A(x_{1}, y_{1})$,$B(x_{2}, y_{2})$ and $C(x_{3}, y_{3})$ are the vertices of $\triangle ABC$.
$(i)$ The median from $A$ meets $BC$ at $D$. Find the coordinates of the point $D$.
$(ii)$ Find the coordinates of the point $P$ on $AD$ such that $AP : PD = 2 : 1$.
$(iii)$ Find the coordinates of points $Q$ and $R$ on medians $BE$ and $CF$,respectively,such that $BQ : QE = 2 : 1$ and $CR : RF = 2 : 1$.
$(iv)$ What are the coordinates of the centroid of the triangle $ABC$?