For it to be a rhombus the slopes of the rhombus need to be opposite reciprocal. Therefore,
[tex]\begin{gathered} \text{slope AB=}\frac{5-0}{4+2}=\frac{5}{6} \\ \text{slope AC=}\frac{1-4}{2-0}=-\frac{3}{2} \end{gathered}[/tex]
Since the slopes are not opposite reciprocal the figure above is not a rhombus. Note this will make the diagonal non-perpendicular.
