Prove that the point A(1, 3, 0), B(-5, 5, 2), C(-9, -1, 2) and D(-3, -3, 0) taken in order are the vertices of a parallelogram. Also, show that ABCD is not a rectangle.

Given:

The points

   

and

   

We know that, opposite sides of both parallelogram and rectangle are equal.

But diagonals of a parallelogram are not equal whereas they are equal for rectangle.

By using the formula,

The distance between any two points

   

is given by,

It is clear that,

   

   

Opposite sides are equal

Now, let us find the length of diagonals

By using the formula,

It is clear that,

   

The diagonals are not equal, but opposite sides are equal.

So we can say that quadrilateral formed by

   

is a parallelogram but not a rectangle.

Hence Proved.