check the picture below.
[tex]\bf \left. \qquad \right.\textit{internal division of a line segment}
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A(0,4)\qquad B(6,8)\qquad
\qquad 1:2\quad \textit{ from A to B}
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\cfrac{AP}{PB} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(0,4)=1(6,8)
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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{(2\cdot 0)+(1\cdot 6)}{1+2}\quad ,\quad \cfrac{(2\cdot 4)+(1\cdot 8)}{1+2}\right)
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P=\left( \cfrac{0+6}{3}~,~\cfrac{8+8}{3} \right)[/tex]
