A line can be divided in proportions using ratios. The point at which a line is divided in ratios is calculated using: [tex][\frac{mx_2+ nx_1}{m+n},\frac{my_2+ ny_1}{m+n}][/tex]
- The coordinate of S is: [tex](6,\frac{8}{3})[/tex]
Given that:
[tex]RS : ST = 5 : 1[/tex]
The coordinates of RT are not given. So, I will solve using a general explanation.
When a line is divided into ratios, the point (S) at which the line is divided is calculated using the following line ratio formula:
[tex]S = [\frac{mx_2+ nx_1}{m+n},\frac{my_2+ ny_1}{m+n}][/tex]
Assume the coordinate of R and T is:
[tex]R = (1,6)\\T = (7,2)[/tex]
[tex]RS : ST = 5 : 1[/tex] means:
[tex]m:n = 5:1[/tex]
So, point S is:
[tex]S = [\frac{5\times 7+ 1 \times 1}{5+1},\frac{5 \times 2+ 1 \times 6}{5+1}][/tex]
[tex]S = [\frac{36}{6},\frac{16}{6}][/tex]
[tex]S = [6,\frac{8}{3}][/tex]
Hence, if the coordinates of R and T are:
[tex]R = (1,6)\\T = (7,2)[/tex]
And the line ratio is:
[tex]m:n = 5:1[/tex]
The coordinate of S is:
[tex]S = [6,\frac{8}{3}][/tex]
Read more about line ratios at:
https://brainly.com/question/3148758
