Question

Os pontos A(-8,y), b(-2,-1) e C (1,-3) são alinhados. encontre a ordenada do ponto A.

Answer 1

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

$\Large\boxed{\begin{array}{l}\sf\begin{vmatrix}\sf-8&\sf y&\sf1\\\sf-2&\sf-1&\sf1\\\sf1&\sf-3&\sf1\end{vmatrix}=0\\\sf -8(-1+3)-y(-2-1)+1(6+1)=0\\\sf-16+3y+7=0\\\sf 3y=16-7\\\sf 3y=9\\\sf y=\dfrac{9}{3}\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf y=3}}}}\end{array}}$