Answer:
[tex]C = (\frac{21}{5},\frac{33}{5})[/tex]
Step-by-step explanation:
Given
Points: (1, 9) and (9, 3)
Ratio = 2/3
Required
Determine the coordinate of the center
Represent the ratio as ratio
[tex]Ratio = 2:3[/tex]
The new coordinate can be calculated using
[tex]C = (\frac{mx_2 + nx_1}{n + m},\frac{my_2 + ny_1}{n + m})[/tex]
Where
[tex](x_1,y_1) = (1, 9)[/tex]
[tex](x_2, y_2) = (9, 3)[/tex]
[tex]m:n = 2:3[/tex]
Substitute these values in the equation above
[tex]C = (\frac{2 * 9 + 3 * 1}{3 + 2},\frac{2 * 3 + 3 * 9}{2 + 3})[/tex]
[tex]C = (\frac{18 + 3}{5},\frac{6 + 27}{5})[/tex]
[tex]C = (\frac{21}{5},\frac{33}{5})[/tex]
Hence;
The coordinates of the new center is [tex]C = (\frac{21}{5},\frac{33}{5})[/tex]
