$\text{ The area of the parallelogram formed by the lines }y=mx\text{ , }y=mx+1,y=nx,\text{ and }y=nx+1\text{ equals }$

$$\begin{gathered} y - mx is a line through (0, 0) andy - mx+ 1 is a line Parallel to y - mx having y-intercePt 1 . \\ The vertices are O(0, 0), X\text{'} A\left(ll\right(m - n), ml(m - n\left)\right). \\ The areaof paralle\log ram is given by \end{gathered}$$

$\begin{array}{c}2\times \mathrm{Ar}\left(\mathrm{\Delta }OAB\right)\\ =2\times \frac{1}{2}\left|\begin{array}{lll}0& 0& 1\\ 0& 1& 1\\ \frac{1}{m-n}& \frac{m}{m-n}& 1\end{array}\right|\\ =\frac{1}{|m-n|}\end{array}$