Explanation

(b)
The equation of lines are
$y - y_{1} = \frac{m_{1} \pm m_{2}}{1 \mp m_{1}m_{2}}\left( x - x_{1} \right)$
Since, $m_{1} = 1,\ \ m_{2} = 1$
$\therefore y - 4 = \frac{1 \pm 1}{1 \mp 1}(x - 3)$
$\Rightarrow y = 4\ or\ x = 3$
Hence, the lines which make the triangle are $x - y = 2,\ x = 3$ and $y = 4$
The intersection points of these lines are (6, 4) , (3, 1) and (3, 4)
$\therefore$ Area of triangle
$= \frac{1}{2}\left| 6(1 - 4) + 3(4 - 4) + 3(4 - 1) \right|$
$= \frac{1}{2}\left| 6( - 3) + 3(0) + 3(3) \right|$
$= \frac{1}{2}| - 18 + 0 + 9| = \frac{9}{2}\ sq\ unit\$