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(C) The given equation $|x| = |y|$ represents the pair of lines $x = y$ and $x = -y$,which can be written as $x - y = 0$ and $x + y = 0$.To find the b

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$y = 0$ and $x = 0$

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(C) The given equation $|x| = |y|$ represents the pair of lines $x = y$ and $x = -y$,which can be written as $x - y = 0$ and $x + y = 0$.To find the bisectors of the angles between these lines,we use the formula $\frac{x - y}{\sqrt{1^2 + (-1)^2}} = \pm \frac{x + y}{\sqrt{1^2 + 1^2}}$.This simplifies to $\frac{x - y}{\sqrt{2}} = \pm \frac{x + y}{\sqrt{2}}$,which implies $x - y = \pm (x + y)$.Taking the positive sign: $x - y = x + y \implies 2y = 0 \implies y = 0$.Taking the negative sign: $x - y = -(x + y) \implies x - y = -x - y \implies 2x = 0 \implies x = 0$.Thus,the equations of the bisectors are $x = 0$ and $y = 0$.

The equation of bisectors of the angles between the lines $|x| = |y|$ are

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