Question

Am A(1,1) B(3,2) C(m,3) ....Aflati m pentru care punctele sunt coliniare ..daca ma puteti ajuta va rog

Answer 1

$A=(1,1)$

$B=(3,2)$

$C=(m,3)$

$A,B,C\:coliniare=>$

$\begin{vmatrix} x_{A} & y_{A} & 1\\ x_{B}& y_{B}& 1\\ x_{C}& y_{C}& 1 \end{vmatrix}=0$

$Folosim\:regula\:lui\:Sarrus\::$

$\begin{vmatrix} 1& 1& 1\\ 3& 2& 1\\ m& 3& 1 \end{vmatrix} =0 \\ \: \: 1 \: \: \: \: \: \: 1 \: \: \: \: 1 \\ \: \: 3 \: \: \: \: \: \: 2 \: \: \: \: 1$

$1 \times 2 \times 1 + 3 \times 3 \times 1 + m \times 1 \times 1 - 1 \times 2 \times m - 1 \times 3 \times 1 - 1 \times 1 \times 3 = 0$

$2 + 9 + m - 2m - 3 - 3 = 0$

$- m + 5 = 0$

$- m = - 5 \: | \times ( - 1)$

$m = 5$