Question

Encontre a área do triangulo.

a) A(3, 2), B(1, 0) e C (-1, 2)

Answer 1

Olá !

Conforme sugere o enunciado , calcularemos a área usando seus vértices.

$\left[\begin{array}{ccc}3&2&1\\1&0&1\\-1&2&1\end{array}\right]\begin{array}{cc}3&2\\1&0\\-1&2\end{array}$

Calculando o determinante .

$\mathsf{\textbf{Det}=0-2+2-0-6-2} \\\\\\ \mathsf{\textbf{Det}=0-2+2-0-8} \\\\\\ \mathsf{\textbf{Det}=0-2+2-8} \\\\\\ \mathsf{\textbf{Det}=0-2-6} \\\\\\ \mathsf{\textbf{Det}=0-8} \\\\\\ \boxed{\mathsf{\textbf{Det}=-8}}$

A área é dada por a metade do módulo do determinante.

$\mathsf{A=\dfrac{|Det|}{2}} \\\\\\ \mathsf{A=\dfrac{|-8|}{2}} \\\\\\ \mathsf{A=\dfrac{8}{2}} \\\\\\ \boxed{\boxed{\boxed{\mathsf{A=4~~U.A}}}}$

Portanto , a área desse triângulo é 4 U.A

Espero ter colaborado !!