Given points are A(6, 8), B(3, 7), C(- 2, - 2) and D(1, - 1).
We need to prove that these are the vertices of a parallelogram.
We know that in the lengths of opposite sides are equal in a parallelogram and the lengths of diagonals are not equal.
Let us find the lengths of the sides.
We know that the distance between the points (x1, y1) and (x2, y2) is
Now,
We got AB = CD and BC = DA, these are the vertices of a parallelogram or rectangle.
Now we find the lengths of the diagonals.
We got AC≠BD.
∴ The points form a parallelogram.