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Math Help - perpenicular bisector...?

  1. #1
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    Unhappy perpenicular bisector...?

    find the equation of the perpendicular bisector of (2,-5) and (6,9), expressing your answer in the form: ax + by + c = 0

    thanks for any help i can quite seem to get this one...

    and its in for tomorrow!! gah!
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by pop_91 View Post
    find the equation of the perpendicular bisector of (2,-5) and (6,9), expressing your answer in the form: ax + by + c = 0

    thanks for any help i can quite seem to get this one...

    and its in for tomorrow!! gah!
    Find the midpoint of the line segment through (2, -5) and (6, 9):

    Midpoint=\left(\frac{2+6}{2} \ \ , \ \ \frac{9-5}{2}\right)=(4, 2)

    Find the slope of the line through (2, -5) and (6, 9).

    slope = \frac{9-^-5}{6-2}=\frac{14}{4}=\frac{7}{2}

    The slope of the perpendicular bisector is the negative reciprocal of that slope, so it would be -\frac{2}{7} and pass through the midpoint (4, 2).

    Using y=mx+b and m = -\frac{2}{7} through (4, 2).

    2=-\frac{2}{7}(4)+b

    \frac{22}{7}=b

    y=-\frac{2}{7}x+\frac{22}{7}

    7y=-2x+22

    2x+7y-22=0
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  3. #3
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    thank you soo much!!!!
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  4. #4
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    Hello, pop_91!

    All the necessary information is there ... just dig it up.


    Find the equation of the perpendicular bisector of A(2,-5) and B(6,9),
    expressing your answer in the form: ax + by + c \:=\: 0

    The perpendicular bisector of AB goes through the midpoint of AB
    . . and is perpendicular to AB.


    The midpoint of AB is: . \left(\frac{2+6}{2},\;\frac{\text{-}5+9}{2}\right) \;=\;(4,\:2)


    The slope of AB is: . m_1 \;=\;\frac{9-(\text{-}5)}{6-2} \:=\:\frac{14}{4} \:=\:\frac{7}{2}
    The perpendicular slope is: . m_2 \:=\:\text{-}\frac{2}{7}


    The line through (4,\:2) with slope \text{-}\frac{2}{7} is:
    . . y - 2 \;=\;\text{-}\frac{2}{7}(x - 4) \quad\Rightarrow\quad y - 2 \;=\;\text{-}\frac{2}{7}x + \frac{8}{7}

    Multiply by 7: . 7y - 14 \;=\;\text{-}2x + 8


    . . Therefore: . {\color{blue}2x + 7y - 22 \;=\;0}

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