Question

Punctul 5 de la primul subiect,

Answer 1

$5)xOy$

$A(1,1),B(3,2),C(m,3)$

$A(x_{A},y_{A}),B(x_{B},y_{B}),C(x_{C},y_{C})$

$m=? \: \: \: ,m\:\in\:\mathbb{R} \: stiind\:ca\:A,B,C\:coliniare$

A,B,C coliniare dacă :

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

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

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

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

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

$m = - 5 \: \in \: \mathbb{R}$