Question

Se no plano cartesiano os pontos A(1,-1), B(7,5) e C(-2,6) são vértices de um triângulo
Determine a área do triângulo ABC.

Answer 1

$\Large\boxed{\begin{array}{l}\sf Sejam~A(x_A,y_A),B(x_B,y_B)~e~C(x_C,y_C)\\\sf os~v\acute ertices~de~um~tri\hat angulo.\\\sf A~\acute area~\acute e~dada~por\\\sf A=\dfrac{|det~M|}{2}\\\sf~onde~M=\begin{vmatrix}\sf x_A&\sf y_A&\sf1\\\sf x_B&\sf y_B&\sf1\\\sf x_C&\sf y_C&\sf1\end{vmatrix}\end{array}}}$

$\large\boxed{\begin{array}{l}\sf M=\begin{vmatrix}\sf1&\sf-1&\sf1\\\sf7&\sf5&\sf1\\\sf-2&\sf6&\sf1\end{vmatrix}\\\sf det~M=1\cdot(5-6)+1\cdot(7+2)+1\cdot(42+10)\\\sf det~M=-1+9+52\\\sf det~M=60\\\sf A=\dfrac{|det~M|}{2}\\\\\sf A=\dfrac{60}{2}\\\\\sf A=30~u\cdot a\end{array}}$