Question

dados os pontos A(2,-3), B(4,-1), e C(-1,3), obtenha a area do triangulo de vertice A, B e C.

Answer 1

A area do triangulo é dada por:

$Area=\frac{1}{2}.\left|\begin{array}{ccc}x_a&y_a&1\\x_b&y_b&1\\x_c&y_c&1\end{array}\right| \\\\\\Area=\frac{1}{2}.\left|\begin{array}{ccc}2&-3&1\\4&-1&1\\-1&3&1\end{array}\right| \\\\Area=\frac{1}{2}.\left[\;(2.(-1).1 + 4.3.1 - 1.(-3).1)\;-\;(1.(-1).(-1)+1.3.2+1.(-3).4)\;\right]\\\\Area=\frac{1}{2}.\left[\;(-2 + 12 +3 )\;-\;(1+6-12\;\right]\\\\Area=\frac{1}{2}.\left[\;(13 )\;-\;(-5)\;\right]\\\\Area=\frac{1}{2}.\left[\;18\;\right]\\\\Area=\frac{18}{2}=9$