Show that the diagonals of the parallelogram whose sides are $l x + m y + n = 0, l x + m y + n = 0, m x + l y + n = 0, m x + l y + n = 0$ include an angle $π / 2$ .

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Solution

The distances between two sets of parallel sides is each $\frac{n - n^{'}}{\sqrt (l^{2} - m^{2})}$ i.e. $p_{1} = p_{2}$ hence the Parallelgram is rhombus whose diagonals we know intersect at right angles.

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Similar questions

Show that the diagonals of the parallelogram whose sides are $l x + m y + n = 0$ , $l x + m y + n^{^{'}} = 0$ , $m x + l y + n = 0$ and $m x + l u + n^{^{'}} = 0$ include an angle $\frac{π}{2}$

Q. If the diagonals of the parallelogram whose sides are

l x + m y + n = 0, l x + m y + n^{'} = 0

and

m x + l y + n = 0, m x + l y + n^{'} = 0

includes an angle

θ

, then the value of

θ

Q. The angle between the diagram of a parallelogram whose sides are

l x + m y + n = 0; l x + m y + n^{1} = 0; m x + l y + n = 0; m x + l y + n^{1} = 0

Q. If the diagonals of the parallelogram whose sides are

l x + m y + n = 0, l x + m y + n^{'} = 0

and

m x + l y + n = 0, m x + l y + n^{'} = 0

includes an angle

θ

, then the value of

θ

Q. 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.

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Show that the diagonals of the parallelogram whose sides are lx+my+n=0, lx+my+n=0, mx+ly+n=0, mx+ly+n=0 include an angle π/2.

The distances between two sets of parallel sides is each n−n′√(l2−m2) i.e. p1=p2 hence the Parallelgram is rhombus whose diagonals we know intersect at right angles.

Show that the diagonals of the parallelogram whose sides are $l x + m y + n = 0, l x + m y + n = 0, m x + l y + n = 0, m x + l y + n = 0$ include an angle $π / 2$ .

The distances between two sets of parallel sides is each $\frac{n - n^{'}}{\sqrt (l^{2} - m^{2})}$ i.e. $p_{1} = p_{2}$ hence the Parallelgram is rhombus whose diagonals we know intersect at right angles.