Question

3°) (PUC-SP) A(3,5), B(1,-1) e C(x,-16) pertencem a uma mesma reta, se x for igual a:


a)-5


b)-1


c) -3


d) -4


e) -2
Obs: faça a resolução com cálculos também

Answer 1

$\Large\boxed{\begin{array}{l}\sf Dado~os~pontos~ A(x_A,y_A),B(x_B,y_B)~e~C(x_C,y_C)\\\sf dizemos~que~A,B~e~C~est\tilde ao~alinhados~quando\\\begin{vmatrix}\sf x_A&\sf y_A&\sf1\\\sf x_B&\sf y_B&\sf1\\\sf x_C&\sf y_C&\sf1\end{vmatrix}=\sf0\end{array}}$

$\Large\boxed{\begin{array}{l}\sf\begin{vmatrix}\sf3&\sf5&\sf1\\\sf1&\sf-1&\sf1\\\sf x&\sf-16&\sf1\end{vmatrix}=0\\\sf 3\cdot(-1+16)-5\cdot(1-x)+1\cdot(-16+x)=0\\\sf 45-5+5x-16+x=0\\\sf 5x+x=16-45+5\\\sf 6x=-24\\\sf x=-\dfrac{24}{6}\\\\\sf x=-4\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~d}}}}\end{array}}$