Respuesta :
[tex]\bf \textit{internal division of a line segment using ratios} \\\\\\ C(-3,-2)\qquad D(6,1)\qquad \qquad \stackrel{\textit{ratio from C to D}}{2:1} \\\\\\ \cfrac{C\underline{P}}{\underline{P} D} = \cfrac{2}{1}\implies \cfrac{C}{D} = \cfrac{2}{1}\implies 1C=2D\implies 1(-3,-2)=2(6,1)\\\\[-0.35em] ~\dotfill\\\\ P=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf P=\left(\cfrac{(1\cdot -3)+(2\cdot 6)}{2+1}\quad ,\quad \cfrac{(1\cdot -2)+(2\cdot 1)}{2+1}\right) \\\\\\ P=\left( \cfrac{-3+12}{3}~~,~~\cfrac{-2+2}{3} \right)\implies P=\left( \cfrac{9}{3}~~,~~\cfrac{0}{3} \right)\implies P=(3~~,~~0)[/tex]
