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Math Help - Area Answer Check

  1. #1
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    Area Answer Check

    I need to find the area of of a triangle with the given vertices:

    A(1,1) B(2,2) C(3,-3)

    I found the lengths of these, and used 1/2llallllbllllallllbll.
    Which I got to result in the area equals 12. Is this correct?

    If I do it using area= P1P2P3= 1/2 \begin{bmatrix}x1&y1&1\\x2&y2&1\\x3&y3&1 \end{bmatrix}
    I end up with:

    -1/2 \begin{bmatrix}1&1&1\\2&2&1\\3&-3&1 \end{bmatrix}
    Which can be row reduced to:
    \begin{bmatrix}1&1&1\\0&0&-1\\0&-6&-2 \end{bmatrix}

    I then use cofactor expansion:
    (-1/2)[1 \begin{bmatrix}0&-1\\-6&-2 \end{bmatrix}]
    When I find the determinant of the cofactor i get:
    (-1/2)(-6)
    This gives me 3 as an answer...
    Which way is right? Or are both wrong?
    Last edited by Hellreaver; November 2nd 2008 at 09:02 PM.
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  2. #2
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    Quote Originally Posted by Hellreaver View Post
    I need to find the area of of a triangle with the given vertices:

    A(1,1) B(2,2) C(3,-3)

    I found the lengths of these, and used 1/2llallllbllllallllbll.
    Which I got to result in the area equals 12. Is this correct?

    If I do it using area= P1P2P3= 1/2 \begin{bmatrix}x1&y1&1\\x2&y2&1\\x3&y3&1 \end{bmatrix}
    I end up with:

    -1/2 \begin{bmatrix}1&1&1\\2&2&1\\3&-3&1 \end{bmatrix}
    Which can be row reduced to:
    \begin{bmatrix}1&1&1\\0&0&-1\\0&-6&-2 \end{bmatrix}

    I then use cofactor expansion:
    (-1/2)[1 \begin{bmatrix}0&-1\\-6&-2 \end{bmatrix}]
    When I find the determinant of the cofactor i get:
    (-1/2)(-6)
    This gives me 3 as an answer...
    Which way is right? Or are both wrong?
    I get 3 square units.

    There are any number of area formulae from geometry you can use to get this answer.
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