Find the coordinates of the point which divides the line segment joining the points $(4, -3)$ and $(8, 5)$ in the ratio $3: 1$ internally.

$ABCD$ is a rectangle formed by the points $A(-1, -1)$,$B(-1, 4)$,$C(5, 4)$,and $D(5, -1)$. $P, Q, R$,and $S$ are the mid-points of $AB, BC, CD$,and $DA$ respectively. Is the quadrilateral $PQRS$ a square,a rectangle,or a rhombus? Justify your answer.

Find the area of a rhombus if its vertices are $(3,0), (4,5), (-1,4)$ and $(-2,-1)$ taken in order. (in square units)

If $A (-5, 7)$,$B (-4, -5)$,$C (-1, -6)$,and $D (4, 5)$ are the vertices of a quadrilateral,find the area of the quadrilateral $ABCD$ (in square units).

Find the point on the $x$-axis which is equidistant from $(2, -5)$ and $(-2, 9).$

Find the coordinates of the points which divide the line segment joining $A (-2, 2)$ and $B (2, 8)$ into four equal parts.