Răspuns:
[tex](a)\boldsymbol{ \red{G\bigg(1;\dfrac{7}{3} \bigg) }}[/tex]
[tex](b)\boldsymbol{ \red{G\Big(-2;-1\Big)}}[/tex]
Explicație pas cu pas:
Aplicăm formulele:
a). A(1,4), B(0,-2), C(2,5)
[tex]x_G = \dfrac{x_{A} + x_{B} + x_{C}}{3} = \dfrac{1+0+2}{3} = 1[/tex]
[tex]y_G = \dfrac{y_{A} + y_{B} + y_{C}}{3} = \dfrac{4-2+5}{3} = \dfrac{7}{3}[/tex]
b). A(-7,1), B (2,-1), C(-1,-3)
[tex]x_G = \dfrac{x_{A} + x_{B} + x_{C}}{3} = \dfrac{-7+2-1}{3}= -2[/tex]
[tex]y_G = \dfrac{y_{A} + y_{B} + y_{C}}{3} = \dfrac{1-1-3}{3} = -1[/tex]
✍ Reținem:
Coordonatele centrului de greutate G(xG, yG) ale triunghiului ABC sunt:
[tex]\boldsymbol{ x_G = \dfrac{x_{A} + x_{B} + x_{C}}{3} }[/tex]
[tex]\boldsymbol{ y_G = \dfrac{y_{A} + y_{B} + y_{C}}{3} }[/tex]
