check the picture below.
[tex]\bf \left. \qquad \right.\textit{internal division of a line segment}
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A(-8,13)\qquad B(2,-2)\qquad
\qquad 2:3\textit{ from A to B}
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\cfrac{AP}{PB} = \cfrac{2}{3}\implies \cfrac{A}{B} = \cfrac{2}{3}\implies 3A=2B\implies 3(-8,13)=2(2,-2)\\\\
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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)}\\\\
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[tex]\bf P=\left(\cfrac{(3\cdot -8)+(2\cdot 2)}{2+3}\quad ,\quad \cfrac{(3\cdot 13)+(2\cdot -2)}{2+3}\right)
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P=\left(\cfrac{-24+4}{5}~,~\cfrac{39-2}{5} \right)[/tex]
