The coordinates of point G is (c) (3,1)
The coordinate points are given as:
[tex]\mathbf{E = (0,4)}[/tex]
[tex]\mathbf{F = (1,3)}[/tex]
The ratio is given as:
[tex]\mathbf{m : n = 1 :2}[/tex]
Line ratio is given as:
[tex]\mathbf{(x,y) = \frac{mx_2 + nx_1}{m + n}, \frac{my_2 + ny_1}{m + n}}[/tex]
Point F is at the partitioned point.
So, we have:
[tex]\mathbf{(1,3) = \frac{1 \times x_2 + 2 \times 0}{1 + 2}, \frac{1 \times y_2 + 2 \times 4}{1 + 2}}[/tex]
[tex]\mathbf{(1,3) = \frac{x_2 }{3}, \frac{y_2 + 8}{3}}[/tex]
Multiply through by 3
[tex]\mathbf{(3,9) = (x_2, y_2 + 8)}[/tex]
By comparison, we have:
[tex]\mathbf{x_2 = 3}[/tex]
[tex]\mathbf{y_2 + 8= 9}[/tex]
Subtract 8 from both sides
[tex]\mathbf{y_2 = 1}[/tex]
Hence, the coordinates of point G is (c) (3,1)
Read more about line partitions at:
https://brainly.com/question/3148758
