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Math Help - Analytic Geometry

  1. #1
    Newbie
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    Oct 2006
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    Analytic Geometry

    Hi,
    I have a question, hope you can help.
    Triangle DEF has vertices D(-2,4), E(0,-2) and F(6,2). Determine the equation for AB, the right bisector of DF.
    I know that the answer supposed to be 4x-y=5.

    Thank you very much!
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  2. #2
    Newbie
    Joined
    Oct 2006
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    I got it
    I tried again and found the answer.
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  3. #3
    MHF Contributor
    Joined
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    Quote Originally Posted by Universe View Post
    I got it
    I tried again and found the answer.
    Heck, I'm late again. I type the slowest.

    But since you didn't show your solution, let me post mine, anyway.

    If AB is the perpendicular bisector of DF, then the slope of AB is the negative reciprocal of the slope of DF.

    If AB is the right bisector of DF, then AB passes through the midpoint of DF.

    Slope of DF, m1 = (2-4)/(6 -(-2)) = -2/8 = -1/4
    Hence, the slope of AB, m2 = -(-4/1) = 4 -----------***

    Midpoint of DF = ((-2+6)/2,(4+2)/2) = (2,3) -------***

    Then, the point-slope form of the equation of line AB is
    (y-y1) = m(x-x1)
    (y -3) = 4(x -2)
    y -3 = 4x -8
    y = 4x -8 +3
    y = 4x -5 -----------------answer.
    Or, to follow the supposed-to-be answer,
    5 = 4x -y
    4x -y = 5 ---------------answer.
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