Question

I have to figure out if it is a rhombus based on the slopes

Answer 1

For it to be a rhombus the slopes of the rhombus need to be opposite reciprocal. Therefore,

`\begin{gathered} \text{slope AB=}(5-0)/(4+2)=(5)/(6) \\ \text{slope AC=}(1-4)/(2-0)=-(3)/(2) \end{gathered}`

Since the slopes are not opposite reciprocal the figure above is not a rhombus. Note this will make the diagonal non-perpendicular.