Question

A system of lines is given as y = m_ix + 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 equal –1, c_i can take 0 or 2. Then the area enclosed by all these straight lines is

• A. $\frac { 3 } { \sqrt { 2 } }$( $\sqrt { 2 }$ –1)
• B. $\frac { 3 } { \sqrt { 2 } }$
• C. $\frac { 3 } { 2 }$
• D. None of these

Answer 1

Answer: (C)

$\frac { 3 } { 2 }$

Answer 2

Lines are y = 1, y = 0

y = –x, y = –x + 2

y = x + 1, y = x – 1

Area of OABCDE = area of OBGF (symmetry)

= $\frac { 3 } { 2 }$ × 1 = $\frac { 3 } { 2 }$