Question

If the straight lines y - 2x, y = 2x +1, y =-7x, y = -7x + 1 form the area of the parallelogram (in square units) is

• A. $\frac{1}{3}$
• B. $\frac{2}{9}$
• C. $\frac{1}{9}$
• D. $\frac{1}{4}$
• E. 9

Answer 1

Answer: (C)

Given equation of straight lines are
$y=2x,y=2x+1,y=-7x$
and $y=-7x+1$
Now, draw these lines on paper, we get

Coordinates of $O\to (0,0),B\to (0,1),C\to \left(\frac{1}{9},\frac{2}{9}\right)$
and $A\to \left(-\frac{1}{9},\frac{7}{9}\right)$
$\therefore$ Area of parallelogram
$=2\times$ Area of $\Delta OBC$
$=2\times \frac{1}{2}\left|x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right|$
$=\left|0+0+\frac{1}{9}(0-1)\right|=\frac{1}{9}$