Question

Dados os pontos colineares A(8,n), B(3,2n) e C(-2,9), determine o valor de n. a) -2 b)-1 c) 0 d) 3 e) 6​

Answer 1

$\Large\boxed{\begin{array}{l}\sf Tr\hat es~pontos~A(x_A,y_A),B(x_B,y_B)~e~C(x_C,y_C)\\\sf s\tilde ao~colineares~quando\\\begin{vmatrix}\sf x_A&\sf y_A&\sf1\\\sf x_B&\sf y_B&\sf1\\\sf x_C&\sf y_C&\sf1\end{vmatrix}=0\end{array}}$

 $\large\boxed{\begin{array}{l}\sf\begin{vmatrix}\sf8&\sf n&\sf 1\\\sf 3&\sf2n&\sf1\\\sf-2&\sf9&\sf1\end{vmatrix}=0\\\sf 8 \cdot(2n -9)-n \cdot(3+2)+1\cdot(27+4n)=0\\\sf 16n-72-5n+27+4n=0\\\sf 15n=72-27\\\sf 15n=45\\\sf n=\dfrac{45}{15}\\\sf n=3\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~d}}}}\end{array}}$