(C) The distance between the parallel lines $ℓx + my + n = 0$ and $ℓx + my + n' = 0$ is given by $d_1 = \frac{|n - n'|}{\sqrt{ℓ^2 + m^2}}$.The distanc

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(C) The distance between the parallel lines $ℓx + my + n = 0$ and $ℓx + my + n' = 0$ is given by $d_1 = \frac{|n - n'|}{\sqrt{ℓ^2 + m^2}}$.The distance between the parallel lines $mx + ℓy + n = 0$ and $mx + ℓy + n' = 0$ is given by $d_2 = \frac{|n - n'|}{\sqrt{m^2 + ℓ^2}}$.Since $d_1 = d_2$,the parallelogram is a rhombus.The diagonals of a rhombus intersect at a right angle ($90^{\circ}$ or $\pi / 2$ radians).Therefore,the angle between the diagonals is $\pi / 2$.

Class 11 Mathematics Straight Line Problems related to triangle and quadrilateral

Medium

What is the angle between the diagonals of the parallelogram formed by the lines $ℓx + my + n = 0$,$ℓx + my + n' = 0$,$mx + ℓy + n = 0$,and $mx + ℓy + n' = 0$?

A
$\tan^{-1} \left( \frac{2ℓm}{ℓ^2 + m^2} \right)$
B
$\tan^{-1} \left( \frac{ℓ^2 - m^2}{ℓ^2 + m^2} \right)$
C
$\pi / 2$
D
$\pi / 3$

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Problems related to triangle and quadrilateral

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Medium

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If a straight line $L$ is perpendicular to the line $4x - 2y = 1$ and forms a triangle of area $4 \text{ sq unit}$ with the coordinate axes,then the equation of the line $L$ is

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Let $A(1, 3)$ and $B(2, 5)$ be two points and $C(h, k)$ be a point such that $BC$ is perpendicular to $AC$. If $\angle CAB = \angle CBA$,then $h =$

EasyTS EAMCET 2023

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What is the angle between the diagonals of the parallelogram formed by the lines $ℓx + my + n = 0$,$ℓx + my + n' = 0$,$mx + ℓy + n = 0$,and $mx + ℓy + n' = 0$?

Similar Questions

Two lines are drawn through $(3, 4)$,each of which makes an angle of $45^\circ$ with the line $x - y = 2$. The area of the triangle formed by these lines is:

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