[tex]\bf \left. \qquad \right.\textit{internal division of a line segment}
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A(0,22)\qquad B(11,0)\qquad
\qquad 5:6\quad \textit{from A to B}
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\cfrac{AM}{MB} = \cfrac{5}{6}\implies \cfrac{A}{B} = \cfrac{5}{6}\implies 6A=5B\implies 6(0,22)=5(11,0)\\\\
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[tex]\bf { M=\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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M=\left(\cfrac{(6\cdot 0)+(5\cdot 11)}{5+6}\quad ,\quad \cfrac{(6\cdot 22)+(5\cdot 0)}{5+6}\right)
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M=\left( \cfrac{55}{11}~~,~~\cfrac{132}{11} \right)[/tex]
and surely you know what that is.
