Originally Posted by

**Hellreaver** 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 $\displaystyle \begin{bmatrix}x1&y1&1\\x2&y2&1\\x3&y3&1 \end{bmatrix}$

I end up with:

-1/2$\displaystyle \begin{bmatrix}1&1&1\\2&2&1\\3&-3&1 \end{bmatrix}$

Which can be row reduced to:

$\displaystyle \begin{bmatrix}1&1&1\\0&0&-1\\0&-6&-2 \end{bmatrix}$

I then use cofactor expansion:

(-1/2)[1$\displaystyle \begin{bmatrix}0&-1\\-6&-2 \end{bmatrix}$]

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?