Question

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

• A. $y=\pm x\&x=0$
• B. $x=\frac{1}{2}\&y=\frac{1}{2}$
• C. $y=0\&x=0$
• D. None of these

Answer 1

The correct option is C

$y=0\&x=0$

Finding the equation of bisectors of the angles:

The given equation is

$\left|x\right|=\left|y\right|$

We know that

$\left|x\right|=\left\{\begin{array}{l}x\text{if}x>0\\ -x\text{if}x<0\end{array}\right.$

So, we can write

$$\begin{gathered} \Rightarrow \left|y\right|=\pm x \\ \therefore y=x\text{or}y=-x \end{gathered}$$

Now graphing these two equations

Therefore, from the figure,

We can see that the angle bisector of $y=x$ and $y=-x$ is $x-axis$ and $y-axis$

Then the equation of the $y-axis$ is $x=0$

The equation of $x-axis$ is $y=0$

Hence, option (C) is the correct answer.