Question

2) Determine x de maneira que os pontos A (3,5), B (1,3) e C(x,1), estejam alinhados.

Answer 1

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

$\Large\boxed{\begin{array}{l}\sf\begin{vmatrix}\sf 3&\sf5&\sf1\\\sf1&\sf3&\sf1\\\sf x&\sf1&\sf1\end{vmatrix}=0\\\sf 3\cdot(3-1)-5\cdot(1-x)+1\cdot(1-3x)=0\\\sf 6-5+5x+1-3x=0\\\sf 5x-3x=-6+5-1\\\sf 2x=-2\\\sf x=-\dfrac{2}{2}\\\\\sf x=-1\end{array}}$