Question

b) Um triângulo possui suas coordenadas
conhecidas. Sabe-se que as coordenadas dos
pontos são: P(0,3); Q(2,0) e R(6,4).
A área delimitada por essas coordenadas é de
(A) 10u.a.
(B) 11u.a.
(C) 12u.a.
(D) 13 u.a.
(E) 14u.a.​

Answer 1

$\huge\mathscr{L}=\begin{vmatrix}0&3&1\\2&0&1\\6&4&1\end{vmatrix}$

$\mathsf{det}\mathscr{L}=\mathsf{-3(2-6)+1.8}\\\mathsf{det}\mathscr{L}=\mathsf{12+8}\\\mathsf{det} \mathscr{L}=\mathsf{20}$

$\mathsf{A=\dfrac{|det~\mathscr{L}|}{2}}$

$\mathsf{A=\dfrac{20}{2}}$

$\huge\boxed{\boxed{\boxed{\boxed{\mathsf{A=10~u.a}}}}}$