8)
[tex]\bf \left. \qquad \right.\textit{internal division of a line segment}
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A(x,y)\qquad C(12,5)\qquad
\qquad AB:BC\qquad 3:4\to \frac{3}{4}
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\cfrac{AB}{BC} = \cfrac{3}{4}\implies \cfrac{A}{C}=\cfrac{3}{4}\implies 4A=3C\implies 4(x,y)=3(12,5)
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{ B=\left(\cfrac{\textit{sum of "x" values}}{r1+r2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{r1+r2}\right)}\\\\
-------------------------------\\\\[/tex]
[tex]\bf B=\left(\cfrac{(4\cdot x)+(3\cdot 12)}{3+4}\quad ,\quad \cfrac{(4\cdot y)+(3\cdot 5)}{3+4}\right)=\stackrel{B}{(4,1)}
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\left(\cfrac{4x+36}{7}~,~\cfrac{4y+15}{7} \right)=(4,1)\implies
\begin{cases}
\cfrac{4x+36}{7}=4\\\\
4x+36=28\\
4x=-8\\
\boxed{x=-2}\\
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\cfrac{4y+15}{7}=1\\\\
4y+15=7\\
4y=-8\\
\boxed{y=-2}
\end{cases}[/tex]
