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Math Help - Distance from a point to a line?

  1. #1
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    Distance from a point to a line?

    Find the equation of the lines that bisect the acute and obtuse angles formed by the lines with the given equations.

    y=2/3x+1
    y=-3x-2

    Know I used the formula d= Ax+By+C/square root A^2+B^2
    To get square root for these functions

    So I got (2/3x-1y+1)/(-1.20) and (-3x-1y-2)/(3.162)

    Then when I cross multiply these my answer come up wrong. Can anyone please help me?
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  2. #2
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    y = \dfrac{2}{3} x + 1

    3y = 2x + 3

    2x - 3y + 3 = 0

    \dfrac{2x - 3y + 3}{\sqrt{13}}


    y = -3x - 2

    3x + y + 2 = 0

    \dfrac{3x+y+2}{\sqrt{10}}


    \dfrac{3x+y+2}{\sqrt{10}} - \dfrac{2x - 3y + 3}{\sqrt{13}} = 0

    \left(\dfrac{3}{\sqrt{10}} - \dfrac{2}{\sqrt{13}}\right)x + \left(\dfrac{1}{\sqrt{10}} + \dfrac{3}{\sqrt{13}}\right)y + \left(\dfrac{2}{\sqrt{10}} - \dfrac{3}{\sqrt{13}}\right) = 0

    the above line bisects the obtuse angle ... the bisector of the acute angle will be perpendicular to the above line.
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