Prove that the points (6, 8), (3, 7), (- 2, - 2), (1, - 1) are the vertices of a parallelogram.

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,

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We got AB = CD and BC = DA, these are the vertices of a parallelogram or rectangle.

Now we find the lengths of the diagonals.

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We got AC≠BD.

∴ The points form a parallelogram.