Question

A área do triângulo cujos vertices são (1,2) (3,4) e (4-1) e igual à

A) 6
B) 8
C) 9
D) 10
E) 12

Answer 1

A área de um triangulo, dado tres pontos, pode ser calculada pelo método do determinante, acompanhe:

$Area~=~\frac{1}{2}~.~\left| \left|\begin{array}{ccc}x_a&y_a&1\\x_b&y_b&1\\x_c&y_c&1\end{array}\right| \right| \\\\\\Area~=~\frac{1}{2}~.~\left| \left|\begin{array}{ccc}1&2&1\\3&4&1\\4&-1&1\end{array}\right| \right| \\\\\\Area~=~\frac{1}{2}.\left|~(1~.~4~.~1+3.(-1).1+4.2.1)-(1.4.4+1.(-1).1+1.2.3)~\right|\\\\\\Area~=~\frac{1}{2}.\left|~(4-3+8)-(16-1+6)~\right|\\\\\\Area~=~\frac{1}{2}.\left|~9-21~\right|\\\\\\Area~=~\frac{1}{2}.\left|~-12~\right|\\\\\\Area~=~\frac{12}{2}$

$\boxed{Area~=~6~unidades~de~area}$

Resposta: Letra A