If $A (3,0), B (0,0), C (1,3)$ and $D (4,3),$ then $\square ABCD$ is a $\ldots \ldots \ldots \ldots$

If the centroid of $\Delta ABC$ is $G(3, 3)$ and the vertices are $B(-1, 2)$ and $C(2, -3)$,then find the area of $\Delta ABC$.

Show that $(-2,-3), (6,3), (3,7),$ and $(-5,1)$ are the vertices of a rectangle.

Find the coordinates of the point $Q$ on the $x$-axis which lies on the perpendicular bisector of the line segment joining the points $A(-5, -2)$ and $B(4, -2)$. Name the type of triangle formed by the points $Q, A$ and $B$.

State whether the following statement is true or false. Justify your answer.
Points $A(3, 1)$,$B(12, -2)$,and $C(0, 2)$ cannot be the vertices of a triangle.

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).