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Math Help - Find exact perpendicular distance between two parallel lines

  1. #1
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    Find exact perpendicular distance between two parallel lines

    Find the exact perpendiuclar distance between two parallel lines.
    a)y=3x-2 and y=3x+3
    please explain your answer
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  2. #2
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    Re: Find exact perpendicular distance between two parallel lines

    Quote Originally Posted by roger1505 View Post
    Find the exact perpendiuclar distance between two parallel lines.
    a)y=3x-2 and y=3x+3
    please explain your answer
    There is a formula for the distance from a point to a line. FIND IT!
    Then find a point on one of the parallel line, use that formula to find the distance from that point to the other line.
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  3. #3
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    Re: Find exact perpendicular distance between two parallel lines

    can you please do it. mainly because its a parallel, and i dont know how to sub it in
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  4. #4
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    Re: Find exact perpendicular distance between two parallel lines

    Your teacher did not show how...or you missed classes?
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  5. #5
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    Re: Find exact perpendicular distance between two parallel lines

    i wasnt in class when they taught this, but does anyone know?
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  6. #6
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    Re: Find exact perpendicular distance between two parallel lines

    You can easily use the "formula" for the distance between a point and a line. For example, you have y = 3x-2 so you know that the point (0,-2) is on the line. So use the formula to find the distance between (0,-2) and the line y = 3x-2.


    Or, you can skip the formula and draw the graph. Use geometry.
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  7. #7
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    Re: Find exact perpendicular distance between two parallel lines

    Hi roger1505,

    1 graph the lines
    2 erect a vertical line @x=1. Apoint (1,1) on line y=3x-2 is produced
    3@(1,1) erect a perpendicular to y=3x+3
    4 write an equation for the perpendicular
    5 solve for intersection of 4 and y=3x +3
    6 use distance formula to find question d
    d^2 = delta y^2 + delta x^2 (slope diagram between (1,1) and solution of 5 above

    There is a simple solution using trig and the slope angle of the parallel lines
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  8. #8
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    Re: Find exact perpendicular distance between two parallel lines

    Quote Originally Posted by roger1505 View Post
    i wasnt in class when they taught this, but does anyone know?
    If Ax+By+C=0 is a line where |A|+|B|\ne 0 and P(p,q) is a point then the distance from that point to the line is \frac{|Ap+Bq+C|}{\sqrt{A^2+B^2}}~.
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  9. #9
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    Re: Find exact perpendicular distance between two parallel lines

    Hello, roger1505!

    If you are allowed to use Trigonometry, here is another solution.


    Find the exact perpendicular distance between two parallel lines: . \begin{array}{ccc}y &=& 3x-2 \\ y &=& 3x + 3 \end{array}

    Code:
            |
            |   /
            |  /        /
            | /        /
            |/        /
          A *        /
          : |@*     /
          : |   *  /
          : |     * C
          5 |    /
          : + - / - - - - 
          : |  /
          : | /
          : |/ @
          B * - - - - E
            |
    The two lines have y- intercepts at 3 and -2, and identical slopes.
    AB \,=\,5.
    Draw AC perpendicular to the line through B.

    Let \theta = \angle CBE
    Then the slope of BC \,=\,\tan\theta \,=\,3
    Note that \angle CAB \,=\, \theta.

    We have: . \tan\theta \:=\:\frac{3}{1}\:=\:\frac{\text{opp}}{\text{adj}}
    \theta is in a right triangle with: opp = 3,\;adj = 1
    Hence: . hyp \,=\, \sqrt{10} \quad\Rightarrow\quad \cos\theta \,=\,\tfrac{1}{\sqrt{10}}

    In right triangle ACB\!:\;\;\cos\theta \,=\,\frac{AC}{5} \quad\Rightarrow\quad AC \:=\:5\cos\theta \:=\:5\left(\tfrac{1}{\sqrt{10}}\right)

    Therefore: . AC \:=\:\frac{\sqrt{10}}{2}

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  10. #10
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    Re: Find exact perpendicular distance between two parallel lines

    Quote Originally Posted by roger1505 View Post
    Find the exact perpendiuclar distance between two parallel lines.
    a)y=3x-2 and y=3x+3
    please explain your answer
    As long as we are into spoon feeding, look at reply #8.
    Rewrite line #1 as 3x-y-2=0. Note that (1,6) is on y=3x+3.

    Apply the formula from reply #8: \frac{|3(1)-1(6)-2|}{\sqrt{(3)^2+(-1)^2}}=\frac{5}{\sqrt{10}}=\frac{\sqrt{10}}{2}.
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  11. #11
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    Re: Find exact perpendicular distance between two parallel lines



    This is the best and simplest way of finding the perpendicular distance between two parallel lines. Hope you get it right.
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  12. #12
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    Re: Find exact perpendicular distance between two parallel lines

    What is your point LJ? Already answered 2 months ago...
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