Question

04. calcule a área do triângulo ABC, sendo A(3,2), B(4,3) e C (5,6).

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Answer 1

Resposta:

1

Explicação passo-a-passo:

$A=\left[\begin{array}{ccc} 3&2&1 \\ 4&3&1 \\ 5&6&1 \end{array}\right]$

$\text{Det}~A=3\cdot3\cdot+2\cdot1\cdot5+1\cdot4\cdot6-5\cdot3\cdot1-6\cdot1\cdot3-1\cdot4\cdot2$

$\text{Det}~A=9+10+24-15-18-8$

$\text{Det}~A=2$

A área do triângulo vale:

$S=\dfrac{|\text{Det}~A|}{2}$

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

$S=1$