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Math Help - Big test question

  1. #1
    Davey1
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    Big test question

    Well, my math teacher gave us this question that he told us would be on the math test tomarow. Im not too sure how to do it but I have an idea.

    An underground cable runs from (-20,35) to (-10,-25). Jessica's house is at (40,5). Determine the shortest distance of cable required to connect Jessys house and the underground cable.

    So first what I did was get the slope of the underground wire.
    M=(y2-y1)/(x2-x1). M=-25-35/-10-(-20) M=-6

    Now i know the perp. bisector is 1/6.

    Now i have to get the exuation of the line.
    y=mx+b
    y=5 x=40 m=1/6
    When that was all done i got b=-1 1/3.

    I dont know if that is right but this is where i am stuck at. It would be real great if someone could help me out. Thanks.
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  2. #2
    Member jacs's Avatar
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    the equation of the line in general form for (-20, 35) (-10, -25) is

    6x + y + 85 = 0

    the shortest distance between a point and a line is the perpendicular distance

    6x + y + 85 = 0 (40, 5)

    <br />
d= \frac{|6 * 40 + 1 * 5 + 85|}{\sqrt{6^2 +1^2}}<br />



     <br />
d = \frac{330}{\sqrt{37}} = 54.25<br />
    Last edited by jacs; January 21st 2006 at 10:39 PM. Reason: Just discovered how to use laTex and giving it a whirl
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  3. #3
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    Let me just help explain jacs answer.

    If the equation of the a non-vertical line is Ax+By+C (this is called standard form). And given a point (x_0,y_0) Then the distance from the point to this line is s=\frac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}}.
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  4. #4
    Member jacs's Avatar
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    Unhappy

    opps sorry, i forgot to include the forumla....
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