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Math Help - parallel lines and shortest distance?

  1. #1
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    parallel lines and shortest distance?

    Determine the decimal approximation of the shortest distance between the parallel lines. (answer rounded to two deciaml places)
    3x+4y-8=0
    6x+8y+4=0

    Please help me with the steps...
    Thank you,

    P.S- I keep getting 2 as an answer but im worried im wrong because the question asks for the answer in two decimal aprox.
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  2. #2
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    Quote Originally Posted by missionmom View Post
    Determine the decimal approximation of the shortest distance between the parallel lines. (answer rounded to two deciaml places)
    3x+4y-8=0
    6x+8y+4=0

    Please help me with the steps...
    Thank you,

    P.S- I keep getting 2 as an answer but im worried im wrong because the question asks for the answer in two decimal aprox.
    3x+4y-8=0 ...(1)
    6x+8y+4=0 ...(2)

    These lines are parallel with gradient \frac{-3}{4}


    The shortest ditance between the lines will lie on the normal between the 2 lines. It will be y-y_1 = m_N(x-x_1) Where m_N = \frac{4}{3} with  x_1 = 0 and y_1= 2

    Now we have

    y-2 = \frac{4}{3} (x-0) Now find where this line crosses both (1) and (2) and find the distance between these points.

    The formula for distacne of a straight line is

     <br />
\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}<br />
    Last edited by pickslides; August 31st 2009 at 05:14 PM. Reason: Bad Latex
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  3. #3
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    The distance from the point (p,q) to the line Ax+By+C=0 is given by \frac{|Ap+Bq+C|}{\sqrt{A^2+B^2}}

    So find one point a one of the lines. Then find its distance to the other line.
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  4. #4
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    Have i done something wrong here?

    y=4/3x+2 y=-3/4x-1/2

    [4/3x+2=-3/4x-1/2]x12

    16x+24=-9x-6
    25x=-30

    x=-6/5

    y=-3/4(-6/5)-1/2
    y=9/10

    B(-6/5,9/10) A(0,-1/2)

    Im stuck, when i square these points i get 1.3
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  5. #5
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    Quote Originally Posted by Plato View Post
    The distance from the point (p,q) to the line Ax+By+C=0 is given by \frac{|Ap+Bq+C|}{\sqrt{A^2+B^2}}

    So find one point a one of the lines. Then find its distance to the other line.

    Will this method give the shortest distance between two parallel lines?
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  6. #6
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    Quote Originally Posted by missionmom View Post
    Determine the decimal approximation of the shortest distance between the parallel lines. (answer rounded to two deciaml places)
    3x+4y-8=0
    6x+8y+4=0

    Please help me with the steps...
    Thank you,

    P.S- I keep getting 2 as an answer but im worried im wrong because the question asks for the answer in two decimal aprox.
    The lines are 3x+4y=8
    & 3x+4y=-2 ( i have modified the equation by dividing both sides by 2)

    The shortest distance between two parallel line in the form

    (a1)*x + (b1)*x + c1 = 0
    &
    (a1)*x + (b1)*x + c2 = 0

    will be = mod{ [c1-c2] / [(a1)^2 + (a2)^2]^1/2 }
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