[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-10,-3.5)\qquad B(2,5.5)\qquad \qquad \stackrel{\textit{ratio from A to B}}{5:1} \\\\\\ \cfrac{A\underline{P}}{\underline{P} B} = \cfrac{5}{1}\implies \cfrac{A}{B} = \cfrac{5}{1}\implies 1A=5B\implies 1(-10,-3.5)=5(2,5.5)[/tex]
[tex](\stackrel{x}{-10}~~,~~ \stackrel{y}{-3.5})=(\stackrel{x}{10}~~,~~ \stackrel{y}{27.5})\implies P=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-10+10}}{5+1}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-3.5+27.5}}{5+1} \right)} \\\\\\ P=\left( \cfrac{0}{6}~~,~~\cfrac{24}{6} \right)\implies P=(0~~,~~4)[/tex]
