Area of the parallelogram formed by the lines y = m x , y = m x + 1 , y = n x and y = n x + 1 equals [2001]

Question

Area of the parallelogram formed by the lines $y = m x, y = m x + 1, y = n x$ and $y = n x + 1$ equals [2001]

Smart Achievers · Accepted Answer

(4)

$The vertices, O (0, 0), A (\frac{1}{m - n}, \frac{m}{m - n}), B (0, 1)$

$Area (parallelogram O A B C) = 2 \times area (∆ O A B)$

$= 2 \times \frac{1}{2}$ $| [0 (\frac{m}{m - n} - 1) + \frac{1}{m - n} (1 - 0) + 0 (0 - \frac{m}{m - n})] |$

$= \frac{1}{| m - n |}$

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