Q. 155.0( 5 Votes )

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

To Prove: Given points are of Parallelogram.

Explanation: Let us Assume that we have points, A (– 2, – 1), B(4, 0), C(3, 3) and D(– 3, 2), are joining the sides as AB, BC, CD, and AD.

The formula used: The slope of the line, m =

Now, The slope of Line AB, mAB =

mAB =

The slope of BC, mBC =

mBC =

Now, The slope of Line CD, mCD =

mCD =

Here, We can see that, mAB = mCDand mBC = mAD

i.e, AB CD and BC AD

We know, If opposite side of a quadrilateral are parallel that it is parallelogram.

Hence, ABCD is a Parallelogram.

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