What type of a quadrilateral do the points $A(2, -2)$,$B(7, 3)$,$C(11, -1)$,and $D(6, -6)$ taken in that order,form?

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 a pentagon having the vertices $(1, 5), (-2, 4), (-3, -1), (2, -3),$ and $(5, 1).$

Two vertices of a triangle are $A(2, 1)$ and $B(3, -2)$. The third vertex is $C(x, y)$,where $y = x + 3$. If the area of the triangle is $5$,find the coordinates of the third vertex.

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

Two vertices of a triangle are $(3, -5)$ and $(-7, 4)$. If the centroid of the triangle is $(2, -1)$,then find the coordinates of the third vertex.