Without using distance formula, show that points (– 2, – 1), (4, 0), (3, 3) and (–3, 2) are the vertices of a parallelogram.

Question

Philoid · Accepted Answer

Let the point A( -2, -1) , B (4, 0) , C( 3, 3) and D( -3, 2)

Slope of AB =

Slope of CD =

⇒slope of AB = Slope of CD

⇒ AB ∥ CD

Slope of BC =

Slope of CD =

Slope of BC = Slope of CD

⇒ BC ∥ CD

Thus the pair of opposite sides are quadrilateral are ∥ , hence ABCD is a parallelogram.

Thus A( -2, -1) , B (4, 0) , C( 3, 3) and D( -3, 2) are vertices of a parallelogram.