Question

9- Os pontos A(1,3), B(8,5) e C(10,2) são vértices de um triângulo, nesse caso determine a área desse triângulo usando determinantes.
1 ponto
a) 10,5
b) 11,5
c) 12,5
d) 13,5
e) 14,5

Answer 1

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

$\boxed{\begin{array}{l}\sf A(1,3)~~B(8,5)~~C(10,2)\\\sf M=\begin{vmatrix}\sf1&\sf3&\sf1\\\sf8&\sf5&\sf1\\\sf 10&\sf2&\sf1\end{vmatrix}\\\sf det~M=1\cdot(5-2)-3\cdot(8-10)+1\cdot(16-50)\\\sf det~M=3+6-34\\\sf det~M=-25\\\sf A=\dfrac{|det~M|}{2}\\\sf det~M=\dfrac{|-25|}{2}\\\sf det~M=\dfrac{25}{2}\\\sf det~M=12,5~u\cdot a\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~c}}}}\end{array}}$