Question

sabendo que os pontos A(2,-3),B(x,0) e C(6,8) formam um triângulo de área 18 u.a,calcule o valor de x​

Answer 1

Resposta:

x = 70/11 ou x = -2/11

Explicação passo a passo:

$\frac{1}{2} \left|\begin{array}{cccc}x_A&x_B&x_C&x_A\\\\y_A&y_B&y_C&y_A\end{array}\right|_{+}^{-}=\\\\\\\ \frac{1}{2} \left|\begin{array}{cccc}2&x&6&2\\-3&0&8&-3\end{array}\right|_{+}^{-}=18\\\\\\|2.0+x.8+6(-3)-(-3).x-0.6-8.2|=36\\\\|0+8x-18+3x-0-16|=36\\\\|11x-34|=36\\\\11x-34=36\\\\11x=36+34\\\\11x=70\\\\x=\frac{70}{11}\\ou\\11x-34=-36\\\\11x=-36+34\\\\11x=-2\\\\x=-\frac{2}{11}$