Q. 94.2( 91 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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