Question

Use a determinant to find the area of the
triangle with the given vertices (0, 0), (3, 5),
(5, −2)

Answer 1

For a triangle with vertices \((x_1,y_1)\), \((x_2,y_2)\) and \((x_3,y_3)\), the area is given by
\[A=\left|\frac{1}{2}\begin{vmatrix}x_1&y_1&1\\x_2&y_2&1\\x_3&y_3&1\end{vmatrix}\right|\]
That is, the absolute value of half the determinant of the matrix.