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=(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=(1)/(2)| \left|\begin{array}{ccc}5-3&4-3\\0-3&2-3=\end{array}\right||=(1)/(2)|\left|\begin{array}{ccc}2&1\\-3&-1\end{array}\right||\\\\\\=(1)/(2)|2(-1)-1(-3)|=(1)/(2)|-2+3|=(1)/(2)|1|=(1)/(2)\ (u^2)`