If $A(3, 0), B(4, 5), C(-1, 4)$ and $D(-2, -1)$ be four points in a plane, show that $ABCD$ is a rhombus but not a square.

The area of a triangle $ABC$ is $k {\mathrm{cm}}^2$, whose vertices (in $\mathrm{cm}$) are $A\left(4, 4\right), B\left(0, 0\right)$ and $C\left(6, 2\right)$. Now, find the value of $k$? 

In $∆ABC$, $D$ and $E$ are the midpoints of the sides $BC$ and $AC$, respectively. Find the length of $DE$. Prove that $DE=\frac{1}{2}AB$.

Find the area (in sq. unit) of the triangle formed by joining midpoints of the sides of the triangle whose vertices are $\left(0, -1\right), \left(2, 1\right)$ and $\left(0, 3\right)$.