Answer:
The coordinates of P is;
[tex]P=(7,9)[/tex]Explanation:
We want to find the coordinate of P such that P partitions AB in the ratio 5:1.
Given the coordinates of A and B as;
[tex]\begin{gathered} A(2,4) \\ B(8,10) \end{gathered}[/tex]Let (x,y) represent the coordinates of point P;
[tex]\begin{gathered} \frac{x-2}{8-x}=\frac{5}{1} \\ x-2=5(8-x) \\ x-2=40-5x \\ x+5x=40+2 \\ 6x=42 \\ x=\frac{42}{6} \\ x=7 \end{gathered}[/tex][tex]\begin{gathered} \frac{y-4}{10-y}=\frac{5}{1} \\ y-4=5(10-y) \\ y-4=50-5y \\ y+5y=50+4 \\ 6y=54 \\ y=\frac{54}{6} \\ y=9 \end{gathered}[/tex]Therefore, the coordinates of P is;
[tex]P=(7,9)[/tex]