Find the coordinates of a point $A,$ where $AB$ is the diameter of a circle whose centre is $(2,-3)$ and $B$ is $(1,4).$

Let $A(4, 2)$,$B(6, 5)$,and $C(1, 4)$ be the vertices of $\Delta ABC$. Find the coordinates of points $Q$ and $R$ on medians $BE$ and $CF$ respectively such that $BQ : QE = 2 : 1$ and $CR : RF = 2 : 1$.

If $A(4, 3)$ and $B(8, 9)$,then the midpoint of $\overline{AB}$ is $\ldots \ldots \ldots \ldots .$

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........

Show that the point $(5, 5)$ is the midpoint of the line segment joining $(3, 5)$ and $(7, 5)$.

Find the coordinates of the points of trisection of the line segment joining $(4, -1)$ and $(-2, -3)$.