[tex] r_{G} = \frac{r_{A}+r_{B}+r_{C}}{3} \\ r_{G}= \frac{(-i+3j)+(3i-j)+(-i-j)}{3} \\ r_{G} = \frac{i+j}{3} = \frac{1}{3}i+\frac{1}{3}j [/tex]
=> G([tex] \frac{1}{3}, \frac{1}{3}[/tex])
G(1/3,1/3); A(-1,3);
[tex]GA = \sqrt{ (-1- \frac{1}{3} )^{2} + (3-\frac{1}{3})^{2} } = \sqrt{ (-\frac{4}{3})^{2} +(\frac{8}{3})^{2} } = \sqrt{ \frac{16}{9}+\frac{64}{9} }= \frac{ \sqrt{80} }{3}[/tex]
G(1/3,1/3); B(3,-1);
[tex]GB=\sqrt{( 3 - \frac{1}{3} )^{2} + (-1- \frac{1}{3} )^{2} } = \sqrt{ (\frac{8}{3})^{2} +(- \frac{4}{3})^{2} } = \sqrt{ \frac{64}{9}+ \frac{16}{9} }= \frac{\sqrt{80} }{3}[/tex]
GA=GB.
