Question

Sabendo que os vértices de um triângulo ABC são A (2, –3),B (–2, 1) e C (5, 3), determine a área desse triângulo.

Answer 1

$\boxed{\begin{array}{c}\tt{\underline{\acute{A}rea~do~tri\hat{a}ngulo~em~func_{\!\!,}\tilde{a}o~das~coordenadas}}\end{array}}\\\sf{A(x_A,y_A)~~B(x_B,y_B)~C(x_C,y_C)}\\\sf{M}=\begin{bmatrix}x_A&y_A&1\\x_B&y_B&1\\x_C&y_C&1\end{bmatrix}\\\Large\boxed{\boxed{\boxed{\boxed{\sf{A=\dfrac{|det~M|}{2}}}}}}$

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$\sf{M}=\begin{bmatrix}2&-3&1\\-2&1&1\\5&3&1\end{bmatrix}\\\sf{det~M=2\cdot(1-3)+3\cdot(-2-5)+1\cdot(-6-5)}\\\sf{det~M=-4-21-11=-36}\\\sf{A=\dfrac{|-36|}{2}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{A=18~u\cdot a}}}}}$