Answer :

Given:


The given lines are


a1x + b1y + c1 = 0 … (1)


a1x + b1y + d1 = 0 … (2)


a2x + b2y + c2 = 0 … (3)


a2x + b2y + d2 = 0 … (4)


To prove:


The area of the parallelogram formed by the lines


a1x + b1y + c1 = 0, a1x + b1y + d1 = 0, a2x + b2y + c2 = 0, a2x + b2y + d2 = 0 is sq. units.


Explanation:


The area of the parallelogram formed by the lines a1x + b1y + c1 = 0, a1x + b1y + d1 = 0, a2x + b2y + c2 = 0 and a2x + b2y + d2 = 0 is given below:


Area


a1b2 – a2b1


Area


If the given parallelogram is a rhombus, then the distance between the pair of parallel lines are equal.



Hence proved.


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