Q. A system of lines is given as $y = m_{i}x + c_{i}$ where $m_{i}$ can take any value out of $0,\ 1,\ - 1$ and when $m_{i}$ is positive, then $c_{i}$ can be 1 or $- 1$, when $m_{i}$ equal 0, $c_{i}$ can be 0 or 1 and when $m_{i}$ equals to $- 1$, $c_{i}$ can take 0 or 2. Then, the area enclosed by all these straight line is
A) $\frac{3}{\sqrt{2}}\left( \sqrt{2} - 1 \right)sq\ unit$
B) $\frac{3}{\sqrt{2}}\ sq\ unit$
C) $\frac{3}{2}\ sq\ unit$
D) None of these
Explanation
(c)
Lines are $y = 1,\ y = 0$
$y = - x,\ y = - x + 2$
$y = x + 1,\ y = x - 1$
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Area of $OABCDE =$ area of $OBGF$
$= \frac{3}{2} \times 1 = \frac{3}{2}\ sq\ unit$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.