Question

Os pontos (-3, 2), (-1, 4) e (6, -3) são vértices de um triângulo. A área desse triângulo é: *​

Answer 1

Utilizando o método do determinante, temos:

$Area~=~\frac{1}{2}\,.\,\left\|\begin{array}{ccc}x_A&y_A&1\\x_B&y_B&1\\x_C&y_C&1\end{array}\right\|\\\\\\Area~=~\frac{1}{2}\,.\,\left\|\begin{array}{ccc}-3&2&1\\-1&4&1\\6&-3&1\end{array}\right\|$

$Area~=~\frac{1}{2}\,.\,\left|~(~(-3).4.1+(-1).(-3).1+6.2.1~)\,-\,(~1.4.6+1.(-3).(-3)+1.2.(-1)~)~\right|$

$Area~=~\frac{1}{2}\,.\,\left|~(~-12~+~3~+~12~)\,-\,(~24~+~9~-~2~)~\right|\\\\\\Area~=~\frac{1}{2}\,.\,\left|~(~3~)\,-\,(~31~)~\right|\\\\\\Area~=~\frac{1}{2}\,.\,\left|~3~-~31~\right|\\\\\\Area~=~\frac{1}{2}\,.\,\left|~-28~\right|\\\\\\Area~=~\frac{1}{2}~.~28\\\\\\\boxed{Area~=~14~unidades~de~area}$