Answer :

Given:


The given lines are


lx + my + n = 0 … (1)


mx + ly + n’ = 0 … (2)


lx + my + n’ = 0 … (3)


mx + ly + n = 0 … (4)



To prove:


The diagonals of the parallelogram whose sides are lx + my + n = 0, lx + my + n’ = 0, mx + ly + n = 0 and mx + ly + n’ = 0 include an angle.


Explanation:


Solving (1) and (2), we get,


B


Solving (2) and (3), we get,


C


Solving (3) and (4), we get,


D


Solving (1) and (4), we get,


A


Let m1 and m2 be the slope of AC and BD.




m1m2 = -1


Hence proved, diagonals of the parallelogram intersect at an angle


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