Question
Prove The Theorem : If $\mathrm{A}\left(x_1, y_1\right), \mathrm{B}\left(x_2, y_2\right)$ and $\mathrm{C}\left(x_3, y_3\right)$ are vertices of triangle $A B C$ then the area of triangle is
$
\frac{1}{2}\left|\begin{array}{lll}
x_1 & y_1 & 1 \\
x_2 & y_2 & 1 \\
x_3 & y_3 & 1
\end{array}\right|
$
$
\frac{1}{2}\left|\begin{array}{lll}
x_1 & y_1 & 1 \\
x_2 & y_2 & 1 \\
x_3 & y_3 & 1
\end{array}\right|
$