Question

calcualar a area formada pela região triangular num plano cartesianos sobre os pontos (2,5), (-3,4) e (2, -3)

Answer 1

$\Large\boxed{\begin{array}{l}\sf Seja~\red{A(x_A,y_A),B(x_B,y_B)~e~C(x_C,y_C)}\\\sf os~v\acute ertices~de~um~tri\hat angulo~qualquer\\\sf no~plano~cartesiano.~\acute area~deste~tri\hat angulo\\\sf \acute e~\blue{A=\dfrac{|det~M|}{2}}~onde\\\\\sf M=\begin{vmatrix}\sf x_A&\sf y_A&\sf1\\\sf x_B&\sf y_B&\sf1\\\sf x_C&\sf y_C&\sf1\end{vmatrix}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf A(2,5),B(-3,4)~e~C(2,-3)\\\sf M=\begin{vmatrix}\sf 2&\sf5&\sf1\\\sf -3&\sf4&\sf1\\\sf 2&\sf-3&\sf1\end{vmatrix}\\\\\sf det~M= 2\cdot(4+3)-5\cdot(-3-2)+1\cdot(9-8)\\\sf det~M=14+25+1=30\\\sf A=\dfrac{| det~M|}{2}\\\\\sf A=\dfrac{30}{2}\\\\\sf\blue{ A=15~u\cdot a}\green{\checkmark}\\\huge\boxed{\boxed{\boxed{\boxed{\sf\red{\maltese}~\blue{\mathbb{D}\mathbb{E}\mathbb{U}\mathbb{S}~\mathbb{V}\mathbb{U}\mathbb{L}\mathbb{T}}}}}}\end{array}}$