Q. 134.6( 7 Votes )

Using slopes. Prove that the points A(-2, -1), B(1,0), C(4, 3) and D(1, 2) are the vertices of a parallelogram.

Answer :

The property of parallelogram states that opposite sides are equal.

We have 4 sides as AB,BC,CD,DA

Given points are A(-2,-1),B(1,0),C(4,3) and D(1,2)

AB and CD are opposite sides, and BC and DA are the other two opposite sides.

So slopes of AB = CD and slopes BC = DA

Slope of AB =

The slope of BC =

The slope of CD =

Slope of DA =

Therefore the Slope of AB = Slope of CD and

The slope of BC = Slope of DA

Also, the product of slope of two adjacent sides is not equal to -1, therefore it is not a rectangle.

Hence ABCD is a parallelogram.

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