Answer:
[tex](x,y) = (-2,-3)[/tex]
Step-by-step explanation:
Given
[tex]R = (-6,-5)[/tex]
[tex]S = (4,0)[/tex]
[tex]Ratio = 2:3[/tex]
Required
Determine the coordinate of the line ratio
Line ratio is calculated using:
[tex](x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
In this case
[tex](x_1,y_1) = (-6,-5)[/tex]
[tex](x_2,y_2) = (4,0)[/tex]
[tex]m:n = 2:3[/tex]
The formula becomes:
[tex](x,y) = (\frac{2 * 4 + 3 * -6}{2+3},\frac{2 * 0 + 3 * -5}{2+3})[/tex]
[tex](x,y) = (\frac{8 - 18}{5},\frac{0 - 15}{5})[/tex]
[tex](x,y) = (\frac{-10}{5},\frac{-15}{5})[/tex]
[tex](x,y) = (-2,-3)[/tex]
