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Math Help - Slopes of perpendicular lines..

  1. #1
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    Slopes of perpendicular lines..

    if

    a and 3
    -
    2

    are the slopes of perpendicular lines, a =

    someone wanna explain negative recipricals to me?
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by zoso
    if

    a and 3
    -
    2

    are the slopes of perpendicular lines, a =

    someone wanna explain negative recipricals to me?
    you got it a/2 *3=-1
    a=-2/3

    Malay
    Last edited by malaygoel; July 18th 2006 at 10:19 PM.
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  3. #3
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    Quote Originally Posted by zoso
    if

    a and 3
    -
    2

    are the slopes of perpendicular lines, a =

    someone wanna explain negative recipricals to me?
    What do you mean a=? Are you just using it as another variable to the slope (m)? Usually the slopes of all lines are m=, regardless of them being perpendicular. In your case, the slope of the line perpendicular to a line with the slope of 3/2 would be m=-2/3

    Negative reciprocals are basically just the opposite of the original fraction/whole number (just flip it).

    Examples:
    m=3/1, the negative reciprocal is: -1/3
    m=5/2, the negative reciprocal is: -2/5
    m=-1/5, the negative reciprocal is: 5
    m=-4/5, the negative reciprocal is: 5/4

    Remember, parallel lines have the same slope.

    Hope this helps..
    -NineZeroFive
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  4. #4
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by 905
    What do you mean a=? Are you just using it as another variable to the slope (m)? Usually the slopes of all lines are m=, regardless of them being perpendicular. In your case, the slope of the line perpendicular to a line with the slope of 3/2 would be m=-2/3

    Negative reciprocals are basically just the opposite of the original fraction/whole number (just flip it).

    Examples:
    m=3/1, the negative reciprocal is: -1/3
    m=5/2, the negative reciprocal is: -2/5
    m=-1/5, the negative reciprocal is: 5
    m=-4/5, the negative reciprocal is: 5/4

    Remember, parallel lines have the same slope.

    Hope this helps..
    -NineZeroFive
    the question was if a line with the slope \frac{a}{2} is perpendicular to a line with the slope 3 then what is the value of a?

    which (this is just extending what Malay said) would mean that 3 and \frac{a}{2} are negative reciprocal, which implies that multiplied together they equal -1, now solve for a...

    \frac{a}{2}\times 3=\neg 1

    \frac{a}{2}=\frac{\neg 1}{3}

    \boxed{a=\frac{\neg 2}{3}}

    check:

    \frac{a}{2}\times 3=\neg 1

    \frac{\frac{\neg 2}{3}}{2}\times 3=\neg 1

    \frac{\neg 2}{6}\times 3=\neg 1

    \frac{\neg 6}{6}=\neg 1

    \neg 1=\neg 1


    Interesting use of negative reciprocal:

    Just a bit of info you might like nzf, in a linear equation like y=mx+b to find the x-intercept you multiply the y-intercept by the slopes negative reciprocal.

    ~ Q\!u\!i\!c\!k
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  5. #5
    Super Member malaygoel's Avatar
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    Slope are used to find family of lines.
    You are given a line ax+by+c=0

    Family of lines parallel to the given line
    ax+by+k=0(Same coefficients of x and t means same slope, k is a parameter)

    Family of lines perpendicular to the given line
    bx-ay+k=0
    or, -bx+ay+k=0(Swapping the cofficients of x and y and multiplying anyone of then by -1 gives a perpendicular line, this is due to negative reciprocal)

    Keep Smiling
    Malay
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