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Math Help - Linear Algebra-Two Point form

  1. #1
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    Linear Algebra-Two Point form

    Which one of the following does not describe the line through the points (1,2) and (3,4)?

    i) (x,y)=(1,2)+t(2,2)
    ii) (x,y)=(3,4)+t(2,2)
    iii) (x,y)=(1-t)(1,2)+t(3,4)
    iv) (x,y)=(1,2)+t(3,4)
    v) (x,y)=(1,2)+t(1,1)

    How do i solve this?
    Thanks!
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  2. #2
    MHF Contributor
    Joined
    Apr 2008
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    The direction of the line is indicated by the vector (3, 4) - (1, 2) = <2, 2>.

    Any point on the line plus a multiple of that vector is a valid representation of the line.

    Note that iii) is equivalent to i) after simplifying.

    In short, the "wrong" answer is iv), since <3, 4> is not a multiple of <2, 2>.
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