Question

1- Dados os vértices A(2, 1), B(3, 2) e C(4, 0), determine a área do triângulo ABC. *
3 pontos
a) 3
b) 1,2
c) 1,5
d) -1,5

Answer 1

A área de um triangulo, dadas as coordenadas dos seus três vértices, é dada por:

$Area~=~\dfrac{1}{2}\cdot\left\|\begin{array}{ccc}x_{_A}&y_{_A}&1\\x_{_B}&y_{_B}&1\\x_{_C}&y_{_C}&1\end{array}\right\|$

Substituindo os pontos:

$Area~=~\dfrac{1}{2}\cdot\left\|\begin{array}{ccc}2&1&1\\3&2&1\\4&0&1\end{array}\right\|$

$=~\dfrac{1}{2}\cdot\left|(2\cdot2\cdot1+3\cdot0\cdot1+4\cdot1\cdot1)~-~(1\cdot2\cdot4+1\cdot0\cdot2+1\cdot1\cdot3)\right|$

$=~\dfrac{1}{2}\cdot\left|(4+0+4)~-~(8+0+3)\right|\\\\\\=~\dfrac{1}{2}\cdot\left|(8)~-~(11)\right|\\\\\\=~\dfrac{1}{2}\cdot\left|8-11\right|\\\\\\=~\dfrac{1}{2}\cdot\left|-3\right|\\\\\\=~\dfrac{1}{2}\cdot3\\\\\\=~\boxed{\dfrac{3}{2}~~ou~~1,5}$

Resposta: Letra C