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

Answer: (D)

Let lines $OB:y=mx$
$CA:y=mx+1$
$BA:y=nx+1$
and $OC:y=nx$
The point of intersection $B$ of $OB$ and $AB$ has $x$ coordinate $\frac{1}{m-n}$.

Now, area of a parallelogram $OBAC$
$=2\times$ area of $\Delta OBA$
$=2\times \frac{1}{2}\times OA\times DB=2\times \frac{1}{2}\times \frac{1}{m-n}$
$=\frac{1}{m-n}=\frac{1}{|m-n|}$
depending upon whether $m>n$ or $m<n$.