Q. 214.8( 4 Votes )

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

Answer :

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

The slope of AB =

The slope of CD =

⇒the slope of AB = Slope of CD

⇒ AB ∥ CD

The slope of BC =

The slope of CD =

The 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.**

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