Question

3) Verifique se os pontos A(− 1, 2), B(− 2, 9) e C(0, − 5), estão alinhados.

Answer 1

$\begin{array}{l}\boxed{\text{Os\ pontos\ ( a,b) ,( c,d) ,( e,f) \ estão\ alinhados\ } \Leftrightarrow \begin{vmatrix}a & b & 1\\c & d & 1\\e & f & 1\end{vmatrix} =0}\\\\\therefore \begin{vmatrix}-1 & 2 & 1\\-2 & 9 & 1\\0 & -5 & 1\end{vmatrix} =-9+10-( -4+5)\\\\\Longrightarrow \begin{vmatrix}-1 & 2 & 1\\-2 & 9 & 1\\0 & -5 & 1\end{vmatrix} =0\\\\\therefore \boxed{\boxed{\text{Os\ pontos\ estão\ alinhados}}}\end{array}$