Thread: Find the equations of the two bisectors of the angles

1. Find the equations of the two bisectors of the angles

Find the equations of the two bisectors of the angles for 3x + 4y = 0 and 5x - 12y + 1 = 0

How do I get started on this?

Thanks

2. Originally Posted by differentiate
Find the equations of the two bisectors of the angles for 3x + 4y = 0 and 5x - 12y + 1 = 0

How do I get started on this?

Thanks

Since the angle bisector of two lines is the locus of all points equidistant from both angle's legs , we must have that any point $(x,y)$ on the bisector must be equidistant from both lines, i.e.:

$\frac{|3x+4y|}{5} = \frac{|5x-12y+1|}{169} \Longrightarrow \frac{3x+4y}{5} = \pm \frac{5x-12y+1}{169}$ , one of these is the bisector's equation of the acute angle

and the other one the bisector's eq. of the obtuse one.

Tonio