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Linear function (difficult for me, SAT Math II level)

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  1. Oct 19, 2007 #1
    If point P(m,2m) is 5 units from the line 12x+5y=1, m could equal
    a. 43/11
    b.-3
    c.-65/22
    d.5
    e.3

    The answer is E.


    Explanation given in book:
    - distance = abs(12(m) + 5(2m) -1) / root(144+25) = 5.
    >>> m=3 or -32/11

    I do not understand this explanation (of course finding m from the equation provided in the explanation is no problem, but I don't know how this equation was set up). Could you please help me out?
     
  2. jcsd
  3. Oct 20, 2007 #2
    root(144+25)=13

    solve for m.
     
  4. Oct 21, 2007 #3

    uart

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    It uses the following well know a formula for the perpendicular distance from a point to a line.

    The distance "d" from the point (x1,y1) to the line ax+by+c=0 is given by :

    d = |a x1 + b y1 + c| / sqrt(a^2 + b^2)
     
  5. Oct 21, 2007 #4

    uart

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    Science Advisor

    BTW there are quite a few differnet methods you can use to come up with a formula for the distance from a point to a line. The one quoted above is popular but I prefer the following because it has a simple one line proof based on similar triangles.

    The distance from a given point to the line y=mx + b is given by,

    d = v/sqrt(m^2+1), where v is the vertical distance from the point to the line.
     
  6. Oct 22, 2007 #5
    Thank you very much, uart! I greatly appreciate your help.
     
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