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Math Help - Points and Vectors

  1. #1
    Ari
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    Points and Vectors

    How do i find the coordinates of a point located 3/5 the distance from (-1,7) to (8,-4) ?

    thanks in advance
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  2. #2
    A Plied Mathematician
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    Can you find the line joining those two points?
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  3. #3
    Ari
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    y = (-9/11)x + (68/11) ?
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    Quote Originally Posted by Ari View Post
    How do i find the coordinates of a point located 3/5 the distance from (-1,7) to (8,-4) ?
    In parametric form the line is \ell (t) = \left( {9t - 1, - 11t + 7} \right).
    Let t=\frac{3}{5}.
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  5. #5
    Ari
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    Quote Originally Posted by Plato View Post
    In parametric form the line is \ell (t) = \left( {9t - 1, - 11t + 7} \right).
    Let t=\frac{3}{5}.
    how do we find the equation of lines in parametric form? For example if i have (-1,1,5) and (6,-3,0) how do i get the equation for the line that passes through them?
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  6. #6
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    Quote Originally Posted by Ari View Post
    how do we find the equation of lines in parametric form?
    Consider the points (a,b)~\&~(c,d).

    In parametric form the line is \ell (t) = \left( {(c-a)t +a, (d-b)t + b} \right).
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  7. #7
    Ari
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    Quote Originally Posted by Plato View Post
    Consider the points (a,b)~\&~(c,d).

    In parametric form the line is \ell (t) = \left( {(c-a)t +a, (d-b)t + b} \right).
    is this always true? what about if it is in R3 like (-1,1,5) and (6,-3,0) or any other two sets of numbers.
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  8. #8
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    Quote Originally Posted by Ari View Post
    is this always true? what about if it is in R3 like my example above?
    Consider the points (x_0,y_0,z_0)~\&~(x_1,y_1,z_1).

    In parametric form the line is \ell (t) = \left( {(x_1-x_0)t +x_0, (y_1-y_0)t +y_0},(z_1-z_0)t +z_0 \right).
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  9. #9
    Ari
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    Quote Originally Posted by Plato View Post
    Consider the points (x_0,y_0,z_0)~\&~(x_1,y_1,z_1).

    In parametric form the line is \ell (t) = \left( {(x_1-x_0)t +x_0, (y_1-y_0)t +y_0},(z_1-z_0)t +z_0 \right).
    wow that seems pretty easy..... thanks.
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  10. #10
    Ari
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    Quote Originally Posted by Plato View Post
    In parametric form the line is \ell (t) = \left( {9t - 1, - 11t + 7} \right).
    Let t=\frac{3}{5}.
    i was thinking and is this right? i need it to be (3/5) the DISTANCE from (-1,7) to (8,-4)
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  11. #11
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    Quote Originally Posted by Ari View Post
    i was thinking and is this right? i need it to be (3/5) the DISTANCE from (-1,7) to (8,-4)
    Why don't you try it?
    Use the distance formula. You do know that, don't you?
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  12. #12
    Ari
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    Quote Originally Posted by Plato View Post
    Why don't you try it?
    Use the distance formula. You do know that, don't you?
    lol nevermind i got it a few minutes after i posted it.
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