Respuesta :
[tex]\bf ~~~~~~~~~~~~\textit{internal division of a line segment}
\\\\\\
J(-2,1)\qquad K(4,5)\qquad
\qquad \stackrel{\textit{ratio from J to K}}{3:7}
\\\\\\
\cfrac{J\underline{P}}{\underline{P} K} = \cfrac{3}{7}\implies \cfrac{J}{K} = \cfrac{3}{7}\implies 7J=3K\implies 7(-2,1)=3(4,5)\\\\
-------------------------------[/tex]
[tex]\bf 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)\\\\ -------------------------------\\\\ P=\left(\cfrac{(7\cdot -2)+(3\cdot 4)}{3+7}\quad ,\quad \cfrac{(7\cdot 1)+(3\cdot 5)}{3+7}\right) \\\\\\ P=\left( \cfrac{-14+12}{7}~~,~~\cfrac{7+15}{7} \right)\implies P=\left(-\frac{2}{7}~~,~~\frac{22}{7} \right)\\ ----------\\ P=\left(-\frac{2}{7}~~,~~3\frac{1}{7} \right)[/tex]
[tex]\bf 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)\\\\ -------------------------------\\\\ P=\left(\cfrac{(7\cdot -2)+(3\cdot 4)}{3+7}\quad ,\quad \cfrac{(7\cdot 1)+(3\cdot 5)}{3+7}\right) \\\\\\ P=\left( \cfrac{-14+12}{7}~~,~~\cfrac{7+15}{7} \right)\implies P=\left(-\frac{2}{7}~~,~~\frac{22}{7} \right)\\ ----------\\ P=\left(-\frac{2}{7}~~,~~3\frac{1}{7} \right)[/tex]
