Question

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

Answer 1

$A(-2,-1),B(4,0),C(3,3),D(-3,2)$

$AB=\sqrt{(4+2{)}^2+(0+1{)}^2}=\sqrt{36+1}=\sqrt{37}$

$CD=\sqrt{(3+3{)}^2+(3-2{)}^2}=\sqrt{36+1}=\sqrt{37}$

$BC=\sqrt{(3-4{)}^2+(0-3{)}^2}=\sqrt{1+9}=\sqrt{10}$

$AD=\sqrt{(-3+2{)}^2+(2+1{)}^2}=\sqrt{1+9}=\sqrt{10}$

$\therefore$ Opposite are equal

$\Rightarrow$ Parallelogram