# Prove that the points (– 4, – 1), (– 2, – 4), (4, 0) and (2, 3) are the vertices of a rectangle. To Prove: Given vertices are of the rectangle.

Explanation: We have given points A(– 4, – 1), B(– 2, – 4), C(4, 0) and D(2, 3)

The points are joining in the form of 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 = The slope of AD, mAD = mAD = Here, We can see that, mAB = mCD and mBC = mAD

i.e, AB CD and BC AD

And, mAB×mBC = MCD×mAD = So, that AB BC and CD AD

Hence, ABCD is a Rectangle.

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