[tex]\bf \left. \qquad \right.\textit{internal division of a line segment}
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A(-2,-1)\qquad B(x,y)\qquad
\qquad 2:3
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\cfrac{AC}{CB} = \cfrac{2}{3}\implies \cfrac{A}{B} = \cfrac{2}{3}\implies 3A=2B\implies 3(-2,-1)=2(x,y)\\\\
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{ C=\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 C=\left(\cfrac{(3\cdot -2)+(2\cdot x)}{2+3}\quad ,\quad \cfrac{(3\cdot -1)+(2\cdot y)}{2+3}\right)~~=~~(-3.6~~,~~-3.4)
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C=\left(\cfrac{-6+2x}{5}~~,~~\cfrac{-3+2y}{5} \right)~~~=~~~(-3.6~~,~~-3.4)\\\\
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\cfrac{-6+2x}{5}=-3.6\implies -6+2x=-18\implies 2x=-12
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x=\cfrac{-12}{2}\implies \boxed{x=-6}\\\\
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\cfrac{-3+2y}{5} =-3.4\implies -3+2y=-17
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2y=-14\implies y=\cfrac{-14}{2}\implies \boxed{y=-7}[/tex]
