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Math Help - About Perpendicular Bisectors

  1. #1
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    About Perpendicular Bisectors

    Three Points have coordinates A(1,7), B(7,5) and C(0,-2). Find:
    a) the equation of the perpendicular bisector of AB

    b)the point intersection of this perpendicular bisector nd BC..

    please i treid my best but i keep getting it wrong..i dont undertsand it please help THANKYOU
    Last edited by Isomorphism; December 24th 2009 at 07:48 PM.
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  2. #2
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    Quote Originally Posted by Tawar View Post
    Three Points have coordinates A(1,7), B(7,5) and C(0,-2. Find:
    a) the equation of the perpendicular bisector of AB

    b)the point intersection of this perpendicular bisector nd BC..

    please i treid my best but i keep getting it wrong..i dont undertsand it please help THANKYOU

    This question doesn't belong here but in pre-algebra or (analytic) geometry...anyway:

    a)(i) Calculate the middle point of the segment AB: it is M (4,6).

    (ii)Calculate the slope of the segment AB: -\frac{1}{3}

    (iii) Calculate the equation of the line through M and perpendicular to AB: its slope must be 3, and then the line is y-6=3(x-4)

    b) Evaluate the line on which the segment AB is and then solve the system of linear equations determined by this equation and the one you found in (a-(iii))

    Tonio
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  3. #3
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    Hello, Tawar!

    Three points have coordinates: . A(1,7),\; B(7,5),\;C(0,-2)

    Find:

    a) the equation of the perpendicular bisector of AB.

    The perpendicular bisector of AB passes through the midpoint of AB: . (4,6)

    Its slope is perpendicular to AB: . m_{AB} \:=\:\frac{5-7}{7-1} \:=\:\frac{\text{-}2}{6} \:=\:-\frac{1}{3}

    The slope of the perpendicular bisector is: . m \:=\:+3

    The equation is: . y - 6 \:=\:3(x-4) \quad\Rightarrow\quad y \:=\:3x-6 .[1]




    b) the point intersection of this perpendicular bisector and BC.

    Line BC has slope: . m \:=\:\frac{\text{-}2-5}{0-7} \:=\:1 . and passes through C(0,-2)

    Its equation is: . y - (-2) \:=\:1(x-0) \quad\Rightarrow\quad y \:=\:x-2 .[2]


    For the intersection, equate [1] and [2]: . 3x-6 \:=\:x-2 \quad\Rightarrow\quad x \:=\:2

    . . Substitute into [1]: . y |:=\:3(2)-6 \quad\Rightarrow\quad y \:=\:0

    The intersection is: . (2,0)

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