Question

Dau coronița
Exercițiul 5 punctul A

Answer 1

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

$A(2,1),B(-1,2),G(2,3)$

$C(x_{C},y_{C})= \: ?$

G-centrul de greutate al triunghiului ABC :

$x_{G}=\frac{x_{A}+x_{B}+x_{C}}{3}</p><p>$

$2 = \frac{2 + ( - 1) + x_{C}}{3}$

$2 = \frac{2 - 1 +x_{C}}{3}$

$2 = \frac{1 + x_{C}}{3} = > 1 + x_{C} = 2 \times 3 = > 1 + x_{C} = 6 = > x_{C} = 6 - 1 = 5$

$y_{G}=\frac{y_{A}+y_{B}+y_{C}}{3}$

$3 = \frac{1 + 2 + y_{C}}{3}$

$3 = \frac{3 + y_{C}}{3} = > 3 + y_{C} = 3 \times 3 = > 3 + y_{C} = 9 = > y_{C} = 9 - 3 = 6$

$= > C(5,6)$