Question

Let me know if you need to see the answer choices

Answer 1

The formula for the slope(m) is,

`m=(y_2-y_1)/(x_2-x_1)`

Let us solve for the slope of PQ

`\begin{gathered} P\rightarrow(-2,4) \\ Q\rightarrow(4,5) \end{gathered}`

Therefore,

`\begin{gathered} \text{Slope(m)=}\frac{\text{5-4}}{4--2}=(1)/(4+2)=(1)/(6) \\ \therefore Slope\text{ of PQ=}(1)/(6) \end{gathered}`

Let us now solve for the slope of RS

`\begin{gathered} R\rightarrow(4,2) \\ S\rightarrow(-2,0) \end{gathered}`

Therefore,

`\begin{gathered} \text{Slope of RS=}\frac{\text{0-2}}{-2-4}=(-2)/(-6)=(1)/(3) \\ \therefore\text{Slope of RS}=(1)/(3) \end{gathered}`

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.