Tell whether the points are the vertices of a parallelogram (that is not a rectangle), a rectangle, or neither.

Question

(-7, -1), (2, -10), (16, -3), (7, 8).

Answer 1

Let the points are is vertices of quadrilateral.

Where AB & CD and BC & DA are opposite sides.

Distance between any two points is .

Now we find the distance between given vertices.

A rectangle is a four sided flat shape where every angle is 90 degrees  and opposite sides are equal and parallel.

A parallelogram is a flat shape with opposite sides are parallel and equal in length.

In this case distance betwen opposite sides are not equal.

From the above , we can come to the conclusion that given vertices are neither a rectangle nor a parallelogram.