Prove that the points (3, -2), (4, 0), (6, -3) and (5, -5) are the vertices of a parallelogram.
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.