Question

Equation of angle bisectors between x and y-axis are

• A. $y=\pm x$
• B. $y=\pm 2x$
• C. $y=\pm \frac{x}{2}$
• D. $y=\pm 3x$

Answer 1

The correct option is A

$y=\pm x$

Explanation for the correct option:

Step 1. Find the equation of angle bisector:

As we know,

The equation of the coordinate axes are $x=0$and $y=0$

As the coordinate axis intersect at the $(0,0)$

$\therefore$the axes are perpendicular to each other which means the angle between them is $90°$

So, the angle bisector between the coordinate axes will be at 45° angle and it will pass through the origin.

Step 2. The equation of angle bisector will be:

$y=mx$ .....(1)

$\because m=\tan \theta$

$\therefore m=\tan 45°$

$=1$

Or, $m=\tan (180°-45)$

$=\tan 135°$

$=-1$

From equation (1), we have

$y=x$or

$y=-x$

$\Rightarrow y=\pm x$

Thus, the equation of angle bisector is $\mathit{y}\mathbf{=}\mathbf{\pm }\mathit{x}$.

Hence, Option ‘A’ is Correct.