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Prove that the points (-2,-1),(4,0),(3,3...

Prove that the points `(-2,-1),(4,0),(3,3)and (-3,2)` are the vertices of a parallelogram.

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Let `P(-2,-1)Q(4,0),R(3,3)and S(-3,2)` be the given points. Then it is sufficient to show `PQ||RS and QR||PS.`
We have, `m_(1)` slopw of `PQ=(0-(-1))/(4-(-2))=1/6`
`m_(2)`= Slope of `RS=(2-3)/(-3-3)=(-1)/(-6)=1/6`
`m_(3)` =Slope of `QR=(3-0)/(3-4)=-3`
`m_(4)=` Slope of `PS=(2-(-1))/(-3-(-2))=(3)/(-1)=-3`
Clearly, `m_(1)=m_(2)and m_(3)=m_(4)`
Thus, `PQ||RS and QR||PS`
Hence, PQRS is a parallelogram
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