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Math Help - Parametric Equations II

  1. #1
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    Parametric Equations II

    Find parametric equations to describe the line 3x + 4y = 12. Use your equations to find coordinates for the point that is three-fifths of the way from (4, 0) to (0, 3).

    I can find the parametric equations to describe the line 3x + 4y = 12. I am having trouble using the equations to find coordinates for the point that is three-fifths of the way from (4, 0) to (0, 3).
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by thamathkid1729 View Post
    Find parametric equations to describe the line 3x + 4y = 12. Use your equations to find coordinates for the point that is three-fifths of the way from (4, 0) to (0, 3).

    I can find the parametric equations to describe the line 3x + 4y = 12. I am having trouble using the equations to find coordinates for the point that is three-fifths of the way from (4, 0) to (0, 3).
    Are your equations:

    x=4 \lambda

    y=3(1-\lambda) ?

    If so the required point is obtained by setting \lambda=2/5

    CB
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  3. #3
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    What Captain Black did was find parametric equations such that \lambda= 0 at the point (0, 3) and \lambda= 1 at the point (4, 0). "Three fifths of the way from (4, 0) to (0, 3)" is 1- 3/5= 2/5 of the way from (0, 3) to (4, 0).

    I think I would have been inclined to do it the other way: find parametric equations such that \lambda= 0 gives the point (4, 0), and \lambda= 1 gives the point (0, 3). That way, "three fifths of the way from (4, 0) to (0, 3)" would be simply \lambda= 3/5. Of course, to do that you would use the vector <0- 4, 3- 0>= <-4, 3> as the "direction vector".

    Thamathkid1729, what parametric equations did you get?
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  4. #4
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    The parametric equations I found were:

    x = -4 + 4t
    y = 6 - 3t

    I just found arbitrary parametric equations... Can I still use these equations to find coordinates for the point that is three-fifths of the way from (4, 0) to (0, 3)?
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by thamathkid1729 View Post
    The parametric equations I found were:

    x = -4 + 4t
    y = 6 - 3t

    I just found arbitrary parametric equations... Can I still use these equations to find coordinates for the point that is three-fifths of the way from (4, 0) to (0, 3)?
    Yes, first find the value of $$t_1 that corresponds to (4,0) and then the value of $$t_2 that corresponds to (0,3).

    Then the parameter value corresponding to the required point is:

    t_3=t_1+\frac{3}{5}(t_2-t_1)

    CB
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