Find the point on the $Y$-axis which is equidistant from $(3, 1)$ and $(-2, 5)$.

$\overline{AB}$ is a diameter of a circle having the centre $P$. If $A(5, -6)$ and $B(3, -2)$,then the coordinates of $P = \dots$

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

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 $ABC$?

Find the area of the triangle whose vertices are $(-8, 4), (-6, 6)$ and $(-3, 9).$

$ABCD$ is a parallelogram with vertices $A(x_{1}, y_{1})$,$B(x_{2}, y_{2})$,and $C(x_{3}, y_{3})$. Find the coordinates of the fourth vertex $D$ in terms of $x_{1}, x_{2}, x_{3}, y_{1}, y_{2}$,and $y_{3}$.