Question

find the combined equation of the line bisecting the angles between the co-ordinate Axes​

Answer 1

Answer:

Hence the equation of bisector is y=±x.

Step-by-step explanation:

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

As the coordinate axis intersect at the origin (0,0).

Therefore, the axes are perpendicular to each other and hence the angle between them is 90°.

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

∴ The equation of bisector will be-

y=mx.....(1)

As

m=tanθ

Therefore,

m=tan45°=1 Or m=tan(180°−45)=tan135°=−1

Now, from eq  

n

(1), we have

y=x or y=−x

⇒y=±x

Answer 2

Answer:

The combined equation of the line bisecting the angles between the co-ordinate axes is y=x

Step-by-step explanation:

The equation of y axis is y=0.

The equation of x axis is x=0.

The line bisecting the angle between the co-ordinate axes makes 45° with the positive x axis.

∴ The slope of the line, m= tan 45°

We know that the line passes through the origin.

According to the equation of line having slope m,

m=$\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$

Assuming $(x_{1} ,y_{1} )$ = (0,0),

m =$\frac{y_{} -0 }{x_{} -0 }$= tan45°= 1

∴y=x

The correct answer is y=x.