Question

Area of the parallelogram formed by the lines $y=mx,y=mx+1,y=nx$ and $y=nx+1$ equals :

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

Answer 1

The correct option is D $\frac{1}{|m-n|}$

Given lines

$y=mx$

$y=mx+1$

$y=nx$

$y=nx+1$

So $y=mx$ and $y=mx+1$ are parallel lines with slope $m$

and $y=nx$ and $y=nx+1$ are parallel lines with slope $n$

Area of parallelogram $=Height\times base$

$=\left|\frac{(1-0)(1-0)}{1\times m-n\times 1}\right|$

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