Lines can be divided into segments using ratios. The coordinates of Q when PR is divided into 5:8 is [tex](-4.462,0.154)[/tex]
Given that:
[tex]P (x_1,y_1) = (-6,-6)[/tex]
[tex]R (x_2,y_2) = (-2,10)[/tex]
[tex]m:n = 5:8[/tex] --- the ratio
The coordinate of Q is calculated using the following line ratio formula
[tex]Q = \frac{1}{m+n}(mx_2 + nx_1,my_2 + ny_1)[/tex]
So, we have:
[tex]Q = \frac{1}{5+8}(5\times -2 + 8\times -6,5\times 10 + 8\times -6)[/tex]
[tex]Q = \frac{1}{5+8}(-58,2)[/tex]
[tex]Q = (-58/13,2/13)[/tex]
[tex]Q = (-4.462,0.154)[/tex]
Hence, the coordinates of Q is [tex](-4.462,0.154)[/tex]
Read more about line ratio at:
https://brainly.com/question/3017771
