Question

determine o valor de M para que os pontos A (-1,M), B (0,-3) e C (-4,5) estejam alinhados e calcule o coeficiente angular da reta que passa simultaneamente por estes três pontos​

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Condic_{\!\!,}\tilde ao~de~alinhamento~de~3~pontos}\\\sf Dados~os~pontos~A(x_A,y_A),B(x_B,y_B)~e~C(x_C,y_C)\\\sf dizemos~que~A,B~e~C~est\tilde ao~alinhados\\\sf quando~\begin{vmatrix}\sf x_A&\sf y_A&\sf1\\\sf x_B&\sf y_B&\sf1\\\sf x_C&\sf y_C&\sf1\end{vmatrix}=0\end{array}}$

$\Large\boxed{\begin{array}{l}\sf\begin{vmatrix}\sf-1&\sf M&\sf1\\\sf 0&\sf-3&\sf1\\\sf-4&\sf5&\sf1\end{vmatrix}=0\\\sf -1\cdot(-3-5)-M\cdot(0+4)+1\cdot(0-12)=0\\\sf8-4M-12=0\\\sf4M=12-8\\\sf 4M=4\\\sf M=\dfrac{4}{4}\\\\\sf M=1\\\sf m=\dfrac{5-[-3]}{-4-[-3]}\\\\\sf m=\dfrac{5+3}{-4+3}\\\\\sf m=\dfrac{8}{-1}\\\\\sf m=-8\end{array}}$