Question

A área do triângulo cujos vértices são os pontos
A(1, 2), B(-1, -1) e C(2, -1) em unidades de área é:

Answer 1

Sendo:

$\text{D}=\left[\begin{array}{ccc}x_A&y_A&1\\x_B&y_B&1\\x_C&y_C&1\end{array}\right]$
A área do triângulo é igual a $\text{S}=\dfrac{|\text{D}|}{2}$

$\left|\begin{array}{ccc}1&2&1\\-1&-1&1\\2&-1&1\end{array}\right|~\begin{array}{cc}1&2\\-1&-1\\2&-1\end{array}$

$\text{D}=1\cdot(-1)\cdot1+2\cdot1\cdot2+1\cdot(-1)\cdot(-1)-1\cdot(-1)\cdot2-1\cdot1\cdot(-1)-2\cdot(-1)\cdot1$

$\text{D}=-1+4+1+2+1+2$

$\text{D}=9$

$\text{S}=\dfrac{|\text{D}|}{2}$

$\text{S}=\dfrac{|9|}{2}$

$\text{S}=\dfrac{9}{2}$

$\text{S}=4,5~\text{u}.\text{a}$