Question

verificar se os pontos A, B, e C, são colineares (ou seja, se estão alinhados)

a) A(2,1), B(0,-3) e C(-2,-7) 

b) A(0, 4), B(–6, 2) e C(8, 10)  ​

Answer 1

Resposta:

LETRA B)

Explicação passo-a-passo:

com certeza! 100%

Answer 2

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

$\Large\boxed{\begin{array}{l}\tt a)\\\sf\begin{vmatrix}\sf2&\sf1&\sf1\\\sf0&\sf-3&\sf1\\\sf-2&\sf-7&\sf1\end{vmatrix}\\\sf 2\cdot(-3+7)-1\cdot(0+2)+1\cdot(0-6)\\\sf8-2-6=0\implies est\tilde ao~alinhados.\end{array}}$

$\Large\boxed{\begin{array}{l}\tt b)\\\sf\begin{vmatrix}\sf0&\sf4&\sf1\\\sf-6&\sf2&\sf1\\\sf8&\sf10&\sf1\end{vmatrix}\\\sf -4\cdot(-6-8)+1\cdot(-60-16)\\\sf56-76=-20\ne0\implies n\tilde ao~est\tilde ao~alinhados.\end{array}}$