We know if the quadrilateral is parallelogram if opposite sides are equal.

Let our points be A(3, -2), B(4, 0), C(6, -3) and D(5, -5).

By distance formula,

XY =

For AB,

AB =

=

= units

For BC,

BC =

=

= units

For CD,

CD =

=

= units

For AD,

AD =

=

= units

Here, we observe that AB = CD and AD = BC, which means that the quadrilateral formed by lines joining by points, is parallelogram.