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Math Help - Parametric Equation Help :)

  1. #1
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    Parametric Equation Help :)

    Hey everyone I have just been given this question as homework, but dont know where to start? any help on getting started would be great !

    Thank you

    Work out parametric equations for the straight lines through this pair of points.

    (-4, 2, 0) and (-3, 3, 0).

    x = y= z=
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by lakitu View Post
    Hey everyone I have just been given this question as homework, but dont know where to start? any help on getting started would be great !

    Thank you

    Work out parametric equations for the straight lines through this pair of points.

    (-4, 2, 0) and (-3, 3, 0).

    x = y= z=
    Let the parameter be t.

    We want a function x(t) that gives x the values -4 and -3. Well, this is supposed to make a line, so we need to make x(t) a line. I'm going to have x(t) pass through the points (t, x) = (0, -4) and (1, -3).

    x(t) = mt + b where m = \frac{-3 - -4}{1 - 0} = 1. Now I will plug the point (0, -4) into this:
    x(t) = t + b

    -4 = 0 + b

    b = -4

    So my first parametric function will be x(t) = t - 4.

    Now we need a y(t). Again we must make y(t) linear, but now we also have to pass the function y(t) through the points (t, y) = (0, 2) and (1, 3) so that it matches what x(t) does.

    So y(t) = m't + b' where m' = \frac{3 - 2}{1 - 0} = 1. We easily find that b' = 2, so that
    y(t) = t + 2.

    Notice that changing the parameter t does nothing to the z coordinate of the points on the line. Thus z(t) = 0.

    So the parametric version of your line is:
    (x(t), y(t), z(t)) = (t - 4, t + 2, 0).

    The only difference in any other correct solution is the choice of t values I used. (Recall that I used t = 0 and t = 1.) We could easily have used t = \pi and t = \sqrt{2} or something. That would merely change the scale of the parameter and would still produce a correct solution.

    -Dan
    Last edited by topsquark; November 26th 2006 at 01:02 PM. Reason: Made a boo boo.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by lakitu View Post
    Hey everyone I have just been given this question as homework, but dont know where to start? any help on getting started would be great !

    Thank you

    Work out parametric equations for the straight lines through this pair of points.

    (-4, 2, 0) and (-3, 3, 0).

    x = y= z=
    Given two points P and Q the line through them is L(x)=P+(Q-P)x

    RonL
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  4. #4
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    hey tahnk you for your reply...I dont understand what your writing though, is there anything abit easier to understand?
    Thank you
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  5. #5
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    I get it now thank you for your time its really appreciated gonna go do the rest now
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