Answer:
G(x,y)=(-4,0)
Step-by-step explanation:
We use the section formula:
[tex](x,y)=\left(\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}\right)[/tex]
Given:
[tex]F(x_1,y_1)=(0, -10)\\H(x_2,y_2)=(-6, 5)\\FG:GH=m:n=2:1[/tex]
We substitute the values to get:
[tex]G(x,y)=\left(\dfrac{2*-6+1*0}{2+1}, \dfrac{2*5+1*-10}{2+1}\right)\\=\left(\dfrac{-12}{3}, \dfrac{10-10}{3}\right)\\=\left(\dfrac{-12}{3}, \dfrac{0}{3}\right)\\\\G(x,y)=(-4,0)[/tex]
