Answer:
[tex]\boxed{P(\frac{67}{9},-\frac{85}{9})}[/tex]
Explanation:
Here we have the following points:
[tex]A(3,-5) \\ \\ B(13,-15)[/tex]
So we want to know the point [tex]P[/tex] which is 4/5 of the way from A to B. So we can calculate this point as follows:
[tex]P( \frac {mx_{\,2} + nx_{\,1} }{m + n},\frac {my_{\,2} + ny_{\,1} }{m + n} )[/tex]
Where:
[tex]m:n=4:5 \\ \\ (x_{1},y_{1})=(3,-5) \\ \\ (x_{2},y_{2})=(13,-15) \\ \\ \\ Then: \\ \\ P( \frac {4(13) + 5(3)}{4+5},\frac {4(-15) + 5(-5) }{4+5} ) \\ \\ \boxed{P(\frac{67}{9},-\frac{85}{9})}[/tex]
