Question

A área de um triângulo de vértice A(5,4), B(7,-2) e C(1,2) é:

Answer 1

Resposta:

$\textrm{A}_{\Delta \textrm{ABC}}=14$

Explicação passo-a-passo:

$\textrm{A}_{\Delta \textrm{ABC}}=\dfrac{\left|\left|\begin{array}{ccc}5&4&1\\7&-2&1\\1&2&1\end{array}\right|\right| }{2} \\\\\\\textrm{A}_{\Delta \textrm{ABC}}=\dfrac{\left| 5.(-2).1+4.1.1+1.7.2-1.(-2).1-2.1.5-1.7.4 \right| }{2} \\\\\\\\\textrm{A}_{\Delta \textrm{ABC}}=\dfrac{\left| -10+4+14+2-10-28 \right| }{2} \\\\\\\\\textrm{A}_{\Delta \textrm{ABC}}=\dfrac{\left| -28 \right| }{2} \\\\\\\\\textrm{A}_{\Delta \textrm{ABC}}=\dfrac{28}{2} \\\\\\\\\textrm{A}_{\Delta \textrm{ABC}}=14$

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