Question

4) Determine o valor de m para que os pontos abaixo sejam alinhados: A(3, 7); B(x, 3) e C(5, -1)​

Answer 1

$\large\boxed{\begin{array}{l}\sf Dados~os~pontos~A(x_A,y_A),B(x_B,y_B)~e~C(x_C,y_C)\\\sf dizemos~que~est\tilde ao~alinhados~quando\\\begin{vmatrix}\sf x_A&\sf y_A&\sf1\\\sf x_B&\sf y_B&\sf1\\\sf x_C&\sf y_C&\sf1\end{vmatrix}=0\end{array}}$

$\large\boxed{\begin{array}{l}\rm Determine~o~valor~de~x~para~que~os~pontos\\\rm abaixo~sejam~ alinhados: A(3,7);B(x,3)~e~C(5,-1)\end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\rm soluc_{\!\!,}\tilde ao\!:}\\\begin{vmatrix}\sf3&\sf7&\sf1\\\sf x&\sf3&\sf1\\\sf 5&\sf-1&\sf1\end{vmatrix}=0\\\sf 3\cdot(3+1)-7\cdot(x-5)+1\cdot(-x-15)=0\\\sf 12-7x+35-x-15=0\\\sf 7x+x=35-15+12\\\sf 8x=32\\\sf x=\dfrac{32}{8}\\\sf x=4\end{array}}$