Explanation

(c)
The equation of lines are $\pm x \pm y = 0.$ Now, we take the lines $x + y = 0$ and $x - y = 0.$
$\therefore$ The equation of bisector 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 negative sign, $x + y = - (x - y) \Rightarrow x = 0$