check the picture below.
so say the point P cuts the segment XY to a ratio of 5:3 from X to Y, thus
[tex]\bf ~~~~~~~~~~~~\textit{internal division of a line segment}
\\\\\\
X(-10,-1)\qquad Y(5,15)\qquad
\qquad 5:3
\\\\\\
\cfrac{X\underline{P}}{\underline{P}Y} = \cfrac{5}{3}\implies \cfrac{X}{Y} = \cfrac{5}{3}\implies 3X=5Y\implies 3(-10,-1)=5(5,15)\\\\
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{ P=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}\\\\
-------------------------------[/tex]
[tex]\bf P=\left(\cfrac{(3\cdot -10)+(5\cdot 5)}{5+3}\quad ,\quad \cfrac{(3\cdot -1)+(5\cdot 15)}{5+3}\right)
\\\\\\
P=\left( \cfrac{-30+25}{8}~~,~~\cfrac{-3+75}{8} \right)\implies P=\left( \cfrac{-5}{8}~~,~~\cfrac{72}{8} \right)
\\\\\\
P=\left( -\frac{5}{8}~~,~~ 9\right)[/tex]
