Point P(x,y) divides the segment AB in the ratio m:n if it has coordinates:
[tex]P(x,y)=(\frac{m_{}x_2+n_{}x_1}{m+n},\frac{my_2+ny_1}{m+n})[/tex]
where A(x1,y1) and B(x2,y2).
In this case we have the ratio 1:4, this means that m=1 and n=4. Plugging this and the coordinates of points A and B we have:
[tex]\begin{gathered} P(x,y)=(\frac{1\cdot3+4\cdot8}{1+4},\frac{1\cdot(-2)+4\cdot(0)}{1+4}) \\ P(x,y)=(\frac{3+32}{5},\frac{-2}{5}) \\ P(x,y)=(\frac{35}{5},-\frac{2}{5}) \\ P(x,y)=(7,-\frac{2}{5}) \end{gathered}[/tex]
Therefore the coordinates of the point P are (7,-2/5)
