Question

Find the area of a triangle with vertices of A(3, 3), B(5, 4), and C(0, 2).

Answer 1

$A(x_A;\ y_A);\ B(x_B;\ y_B);\ C(x_C;\ y_C)\\\\A_\Delta=\frac{1}{2}| \left|\begin{array}{ccc}x_B-x_A&y_B-y_A\\x_C-x_A&y_C-y_A\end{array}\right||\\=================================\\A(3;\ 3);\ B(5;\ 4);\ C(0;\ 2)\\\\A_\Delta=\frac{1}{2}| \left|\begin{array}{ccc}5-3&4-3\\0-3&2-3=\end{array}\right||=\frac{1}{2}|\left|\begin{array}{ccc}2&1\\-3&-1\end{array}\right||\\\\\\=\frac{1}{2}|2(-1)-1(-3)|=\frac{1}{2}|-2+3|=\frac{1}{2}|1|=\frac{1}{2}\ (u^2)$