Question

graph the quadrilateral with the given vertices in a coordinate plane. then show the quadrilateral in a a parallelogram

Answer 1

First, let's graph the polygon:

Now, let's prove it's a parallelogram by showing that the segments NP and RQ are parallel, and NR and PQ are parallel as well.

Let's prove that the angular coefficient is the same for NR and PQ

`\begin{gathered} m_(NR)=(0-(-4))/(-5-(-3))=-(4)/(3) \\ \\ m_(PQ)=(5-0)/(0-3)=-(4)/(3) \end{gathered}`

Then they're parallel, just to confirm, let's do the same for NP and RQ

`\begin{gathered} m_(NP)=(4-0)/(0-(-5))=(4)/(5) \\ \\ m_(RQ)=(-4-0)/(-2-(3))=(4)/(5) \end{gathered}`

Then it's parallel as well.