Question

Point F is at (0, -10) and point H is at (-6, 5). Find the coordinates of point G on line segment FH such that the ratio of FG to GH is 2 : 1

Answer 1

G(x,y)=(-4,0)

Explanation:

We use the section formula:

`(x,y)=\left((mx_2+nx_1)/(m+n), (my_2+ny_1)/(m+n)\right)`

Given:

`F(x_1,y_1)=(0, -10)\\H(x_2,y_2)=(-6, 5)\\FG:GH=m:n=2:1`

We substitute the values to get:

`G(x,y)=\left((2*-6+1*0)/(2+1), (2*5+1*-10)/(2+1)\right)\\=\left((-12)/(3), (10-10)/(3)\right)\\=\left((-12)/(3), (0)/(3)\right)\\\\G(x,y)=(-4,0)`