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Math Help - Parametrizing a line segment

  1. #1
    Member
    Joined
    Jan 2008
    Posts
    118

    Parametrizing a line segment

    I am given two points.
    (-2,5) and (4,3)


    I kind of understand the concept, but am not totally clear.
    I know I use...

    x= x + at
    y= y + bt

    I dont get where to put the x's and y's...and what to use for t. How do I know which is which when t = 0 or t = 1?
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  2. #2
    Senior Member
    Joined
    Nov 2008
    Posts
    461
    Hi Morgan82!

    Quote Originally Posted by Morgan82 View Post
    I am given two points.
    (-2,5) and (4,3)


    I kind of understand the concept, but am not totally clear.
    I know I use...

    x= x + at
    y= y + bt
    No, thats not true.

    point has the coordinates (t,y), then the equation is

    y = a + t*x

    There are two points (-2,5) and (4,3), this leads to

    5 = a+(-2)x
    e.g.

    5 = a - 2x (eq 1)

    3 = a + 4*x (eq 2)

    and now you need to solve the equations, like this

    (eq1) - (eq2)


    5-3 = a -2x - (a +4x)

    2 = a -2x - a - 4x

    2 = -6x

    x = -1/3

    Now you know x and substitute it in eq 1 (substitute in eq 2 would work, too)

    5 = a - 2*(-1/3) (x=-1/3 in eq 1)

    5 = a + 2/3

    5 - 2/3 = 13/3 = a

    So the solution is y = 13/3 -1/3*x


    Do you understand?

    Yours
    Rapha

    Quote Originally Posted by Morgan82 View Post
    I dont get where to put the x's and y's...and what to use for t. How do I know which is which when t = 0 or t = 1?
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