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Math Help - Find the equations of the two bisectors of the angles

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by differentiate View Post
    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
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