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 $O B: y=m x$
$C A: y =m x+1 $
$B A: y =n x+1$
and $ O C: y =n x$
The point of intersection $B$ of $O B$ and $A B$ has $x$ coordinate $\frac{1}{m-n}$.

Now, area of a parallelogram $O B A C$
$=2 \times $ area of $ \Delta O B A $
$=2 \times \frac{1}{2} \times O A \times D B =2 \times \frac{1}{2} \times \frac{1}{m-n} $
$=\frac{1}{m-n}=\frac{1}{|m-n|}$
depending upon whether $m>n$ or $m < n$.