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) = (x_{1}, y_{1}); B (5,5) = (x_{2}, y_{2});

C (2,4) = (x_{3}, y_{3}) and D (1,7) = (x_{4}, y_{4})

Distance between two points P (x_{1}, y_{1}) and Q (x_{2}, y_{2}) =

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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