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Parameterizing a line

  1. Apr 22, 2012 #1
    1. The problem statement, all variables and given/known data

    Parameterize a line, L, such that is crosses through the point P=(3, -5) and direction v=(2, 8). Now, using this parametrization determine the following points belong to L: P1=(73, -180) and P2=(5, -14)

    2. Relevant equations



    3. The attempt at a solution
    I really need help with this type of questions in major need of help and explanations.
     
  2. jcsd
  3. Apr 22, 2012 #2

    tiny-tim

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    welcome to pf!

    hi vanitymdl! welcome to pf! :smile:

    let's start with the first part

    can you do …
     
  4. Apr 22, 2012 #3
    okay all I know is where the point is located, so with the direction is it going towards that point?
     
  5. Apr 22, 2012 #4

    sharks

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    The line L passes through the point P and has direction v, so it goes away from the point P, say, to another point Q on its path.
     
  6. Apr 22, 2012 #5
    Oh so that line is going to stop at (2,8)?
     
  7. Apr 22, 2012 #6

    tiny-tim

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    no, it means that the direction is parallel to the line going through (0,0) and (2,8)

    (its "clock direction" is (2,8))
     
  8. Apr 22, 2012 #7
    okay I think I have an idea now
    since P is (3,-5) and v (2,8)

    then (x,y) = (3,-5) + t(2,8)
    which is (3+2t, -5+8t)

    x = 3+2t
    y = -5+8t
     
  9. Apr 22, 2012 #8

    tiny-tim

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    yup! :biggrin:

    are you ok with the second part now? :smile:
     
  10. Apr 22, 2012 #9
    Ah I'm excited I figured that out. Okay just to clarify the second part, I get my x and y then equal it to the point that I'm trying to figure out if its in the line?
     
  11. Apr 22, 2012 #10
    If my t's for the x and y give me different value does that mean that they don't belong to the line?
     
  12. Apr 22, 2012 #11

    sharks

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    For the same point, t is a constant, so it should stay the same for both x and y.
     
  13. Apr 22, 2012 #12

    tiny-tim

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    again … yup! :biggrin:
     
  14. Apr 22, 2012 #13
    Thank you SO MUCH :)
     
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