Q. 115.0( 5 Votes )

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

Answer :


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 ABBC and CDAD


Hence, ABCD is a Rectangle.


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