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Math Help - Finding the Perpendicular bisector.

  1. #1
    Member MathBlaster47's Avatar
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    Finding the Perpendicular bisector.

    I have another one of those questions I'd like to double check.

    Question:
    What is the perpendicular bisector of the line between points (2,2) and (6,6)?

    Working:
    slope= \frac{6-2}{6-2}=\frac{4}{4}=1
    Since a perpendicular bisector has a reciprocal slope to the line it bisects, the slope of the bisector is -\frac{4}{4}=-1
    The midpoint of the bisected line is (4,4) as shown by the midpoint formula: \frac{x_1+x_2}{2},\frac{y_1+y_2}{2} where x_1=2, x_2=6, y_1=2 and y_2=6. I'll use the point-slope formula to find the line, so:
    let, y_1=4, x_1=4 , and slope=-1, y-y_1=slope(x-x_1)\rightarrow y-4=-1(x-4)\rightarrow y-4=-x+4 \rightarrow -x-y=8.

    Answer:
    The equation of the bisecting line is: -x-y=8

    Is my working and answer correct?
    Last edited by MathBlaster47; February 19th 2010 at 07:11 AM.
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  2. #2
    Member mathemagister's Avatar
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    Quote Originally Posted by MathBlaster47 View Post
    I have another one of those questions I'd like to double check.

    Question:
    What is the perpendicular bisector of the line between points (2,2) and (6,6)?

    Working:
    slope= \frac{2+6}{2},\frac{2+6}{2}=\frac{4}{4}=1
    Since a perpendicular bisector has a reciprocal slope to the line it bisects, the slope of the bisector is -\frac{4}{4}=-1
    The midpoint of the bisected line is (4,4) as shown by the midpoint formula: \frac{x_1+x_2}{2},\frac{y_1+y_2}{2} where x_1=2, x_2=6, y_1=2 and y_2=6. I'll use the point-slope formula to find the line, so:
    let, y_1=4, x_1=4 , and slope=-1, y-y_1=slope(x-x_1)\rightarrow y-4=-1(x-4)\rightarrow y-4=-x+4 \rightarrow -x-y=8.

    Answer:
    The equation of the bisecting line is: -x-y=8

    Is my working and answer correct?

    Hey MathBlaster47! Really good job so far. You did everything perfectly except for the very last step. The correct answer:

    y-4=-x+4 \rightarrow -x-y=-8 \rightarrow x+y=8

    You did everything else very well, well done on the presentation!
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  3. #3
    Member MathBlaster47's Avatar
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    Thanks!
    So I forgot to place the "-" signs where they were needed, effectively skipping a step.
    I see why I was incorrect though, as -4+4 doesn't equal 8--it equals 0!

    I have to present math working like that because it is the only way I understand what I'm saying!
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  4. #4
    Member mathemagister's Avatar
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    Quote Originally Posted by MathBlaster47 View Post
    Thanks!
    So I forgot to place the "-" signs where they were needed, effectively skipping a step.
    I see why I was incorrect though, as -4+4 doesn't equal 8--it equals 0!

    I have to present math working like that because it is the only way I understand what I'm saying!
    You're very welcome.

    And your presentation makes it easy for me to follow you and find out exactly where you went wrong.
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