The formula for the slope(m) is,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let us solve for the slope of PQ
[tex]\begin{gathered} P\rightarrow(-2,4) \\ Q\rightarrow(4,5) \end{gathered}[/tex]
Therefore,
[tex]\begin{gathered} \text{Slope(m)=}\frac{\text{5-4}}{4--2}=\frac{1}{4+2}=\frac{1}{6} \\ \therefore Slope\text{ of PQ=}\frac{1}{6} \end{gathered}[/tex]
Let us now solve for the slope of RS
[tex]\begin{gathered} R\rightarrow(4,2) \\ S\rightarrow(-2,0) \end{gathered}[/tex]
Therefore,
[tex]\begin{gathered} \text{Slope of RS=}\frac{\text{0-2}}{-2-4}=\frac{-2}{-6}=\frac{1}{3} \\ \therefore\text{Slope of RS}=\frac{1}{3} \end{gathered}[/tex]
Hence, the slope of line PQ is 1/6 and the slope of RS is 1/3 so figure PQRS is not a parallelogram because opposite sides are not parallel.
