Without using distance formula, show that points `(-2, -1), `(4, 0)`, `(3, 3)`, and `(-3, 2)` are the vertices of a parallelogram.

Explanation

Let `A=(-2,-1)`, `B=(4,0)` ,`C=(3,3)` and `D=(-3,2)`
The slope of line `AB`, `m_(1)=(0-(-1))/(4-(-2))=(1)/(6)` ,
Slope of line `BC`, `m_(2)=(3-0)/(3-4)=-3`,
Slope of `CD`, `m_(3)=(2-3)/(-3-3)=(-1)/(-6)=(1)/(6)`
Slope of line `DA`, `m_(4)=(2-(-1))/(-3-(-2))=(3)/(-3+2)=-3`
`:' m_(1)=m_(3)implies AB||CD`
and `m_(2)=m_(4)implies BC||DA`
`:.ABCD` is a paralleogram.
Therefore, given points are the vertices of a parallelogram.