Show that $\mathrm{A}(-3,2), \mathrm{B}(-5,-5), \mathrm{C}(2,-3)$ and $\mathrm{D}(4,4)$ are the vertices of a rhombus.

Find the lengths of the medians of a $△\mathrm{ABC}$ having vertices at $\mathrm{A}(0,-1), \mathrm{B}(2,1)$ and $\mathrm{C}(0,3).$

If $\mathrm{P}(4,\mathrm{m})$ divides the line segment joining the points $\mathrm{A}(2,3)$ and $\mathrm{B}(6,-3)$ in the ratio $\mathrm{\lambda }:1$ then find $\mathrm{m}$.