Explanation

(c)
The equation of lines are $x + y = 0$ and $x - y = 0$
$\therefore$ The equation of bisectors of the angles between these lines are
$\frac{x + y}{\sqrt{1 + 1}} = \pm \frac{x - y}{\sqrt{1 + 1}}\ \Rightarrow x + y = \pm (x - y)$
Taking positive sign, $x + y = (x - y)$
$\Rightarrow y = 0$
Taking positive sign, $x + y = - (x - y)$
$\Rightarrow x = 0$
Hence, the equation of bisectors are $x = 0$ and $y = 0$