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Math Help - determinants

  1. #1
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    determinants

    how do you prove that (x1, y1), (x2,y2), (x3,y3) are collinear pts iff det of
    lx1,y1,1l
    lx2,y2,1l
    lx3,y3,1l is 0.

    the above is a 3x3 matrix.
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    how do you prove that (x1, y1), (x2,y2), (x3,y3) are collinear pts iff det of
    lx1,y1,1l
    lx2,y2,1l
    lx3,y3,1l is 0.

    the above is a 3x3 matrix.
    .
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  3. #3
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    sorry, i cant seem to see what you have typed:/
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  4. #4
    Senior Member Shanks's Avatar
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    The area of the triangle formed by the three given point is half of the absolute value of determinant.
    Thus if the three points are colinear, then the determinant is equal to 0.
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  5. #5
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    what does it mean that the area formed by the 3 given pts is half the absolute value of the determinant?

    could you explain further?
    thank you!
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  6. #6
    Senior Member Shanks's Avatar
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    This is the formulla to find the area of a triangle formed by three points whose coordinates are given.
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