Q. 5 B5.0( 1 Vote )

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Answer :

Given: A = (4, 8), B = (5, 5), C = (2, 4), D = (1, 7)


To Prove: AD||BC


AB||DC



Proof:


Let A (4,8) = (x1, y1); B (5,5) = (x2, y2);


C (2,4) = (x3, y3) and D (1,7) = (x4, y4)


Distance between two points P (x1, y1) and Q (x2, y2) =


The slope of the line AB = [Distance formula]


=


= …(i)


The slope of the line DC = [Distance formula]


=


= …(ii)


The slope of the line AD = [Distance formula]


=


= …(iii)


The slope of the line BC = [Distance formula]


=


The slope of line AB = The slope od’s the line DC [From (1) and (2)]


AB||DC


The slope of line AD = The slope of the line BC [From(3) and (4)]


AD||BC


Hence, ABCD is a parallelogram.


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