Assertion :The diagonals of the parallelogram whose sides are $l x + m y + n = 0, l x + m y + n^{'} = 0, m x + l y + n = 0, m x + l y + n^{'} = 0$ are perpendicular. Reason: If the perpendicular distances between parallel sides of a parallelogram are equal, then it is a rhombus.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Reason is correct
Assertion:
Line $l x + m y + n = 0$ and $l x + m y + n^{'} = 0$ are parallel with distance between then is
$\frac{n - n^{'}}{\sqrt{l^{2} + m^{2}}}$ ...(1)
And lines $m x + l y + n = 0$ and $m x + l y + n^{'} = 0$ are parallel with distance between them is
$\frac{n - n^{'}}{\sqrt{m^{2} + l^{2}}}$ ...(2)
From (1) and (2) assertion is true

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