Area of the parallelogram formed by the lines y = mx, y =… — JEE Main 2001 Mathematics PYQ

2001

Area of the parallelogram formed by the lines

y = mx

y = mx + 1

y = nx

and

y = nx + 1

equals

A.
$\dfrac{|m+n|}{(m-n)^2}$
B.
$\dfrac{2}{|m+n|}$
C.
$\dfrac{1}{|m+n|}$
D.
$\dfrac{1}{|m-n|}$

Show answer and solution

Correct option: D

Solution

The distance between the parallel lines y = mx and y = mx+1 is 1/√(1+m²), and between y = nx and y = nx+1 is 1/√(1+n²). The angle θ between the two pairs of lines satisfies sin θ = |m-n|/[√(1+m²)·√(1+n²)]. Area of parallelogram = (base × height) = d₁ × d₂ / sin θ = [1/√(1+m²)] × [1/√(1+n²)] divided by |m-n|/[√(1+m²)·√(1+n²)] = 1/|m-n|.

[2001]

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