# Thread: Bisector of an acute angle (Help)

1. ## Bisector of an acute angle (Help)

Find the equation of the line that bisects the acute angles determined by the given lines.

1) $\displaystyle x-6y-12=0$ and $\displaystyle 4x-6y-9=0$

Attempt:

$\displaystyle d1=\frac{x-6y-12}{-\sqrt{37}}$ , $\displaystyle \frac{4x-6y-9}{-2\sqrt{13}}$
So d1+d2 =0
$\displaystyle d1=\frac{x-6y-12}{-\sqrt{37}}$ +$\displaystyle \frac{4x-6y-9}{-2\sqrt{13}}$

=$\displaystyle \frac{(-4\sqrt{37} -2\sqrt{13} )x +(6\sqrt{37} +12\sqrt{13} )y+(-9\sqrt{37} -24\sqrt{13} )}{2\sqrt{481}}$

How to make the equation free of square roots?
And is my solution correct ( if not please follow the procedure that i have done which is d1+d2=0 )
Thank you.

2. $\displaystyle d1=\frac{x-6y-12}{-\sqrt{37}}$,$\displaystyle \frac{4x-6y-9}{-2\sqrt{13}}$
why you have found distances from the origin?

3. Originally Posted by malaygoel
why you have found distances from the origin?
Oh sorry it should be x prime and y prime.

4. Originally Posted by mj.alawami
Find the equation of the line that bisects the acute angles determined by the given lines.

1) $\displaystyle x-6y-12=0$ and $\displaystyle 4x-6y-9=0$

Attempt:

$\displaystyle d1=\frac{x-6y-12}{-\sqrt{37}}$ , $\displaystyle \frac{4x-6y-9}{-2\sqrt{13}}$
It is
$\displaystyle d1=\frac{|x-6y-12|}{\sqrt{37}}$ , $\displaystyle \frac{|4x-6y-9|}{2\sqrt{13}}$

So d1+d2 =0
so there are two equtions:
d1+d2=0
d1=d2
$\displaystyle d1=\frac{x-6y-12}{-\sqrt{37}}$ +$\displaystyle \frac{4x-6y-9}{-2\sqrt{13}}$
$\displaystyle 0=\frac{x-6y-12}{\sqrt{37}}$ +$\displaystyle \frac{4x-6y-9}{2\sqrt{13}}$
$\displaystyle \frac{x-6y-12}{\sqrt{37}}$ =$\displaystyle \frac{4x-6y-9}{2\sqrt{13}}$

I have not checked calculations...will do in a short time.

5. You have an error in your second equation it should be
d1=-d2