A line segment can be divided into ratios.
The coordinate of P on line segment AB is (5,1)
Given
[tex]A = (-3,-5)[/tex]
[tex]B = (9,4)[/tex]
The position of P from A to B is:
[tex]P_A = \frac 23[/tex]
So, from P to B would be:
[tex]P_B =1 - \frac 23[/tex]
[tex]P_B = \frac 13[/tex]
So, the ratio is:
[tex]m : n = \frac 23 : \frac 13[/tex]
Simplify
[tex]m : n = 2 :1[/tex]
The coordinate of point P is:
[tex]P = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})[/tex]
So, we have:
[tex]P = (\frac{2 \times 9 + 1 \times -3}{2 + 1},\frac{2 \times 4 + 1 \times -5}{2 + 1})[/tex]
[tex]P = (\frac{15}{3},\frac{3}{3})[/tex]
[tex]P = (5,1)[/tex]
Hence, the coordinate of P is (5,1)
Read more about line ratios at:
https://brainly.com/question/8847082
