Check the picture below.
we can also word this as
finding the point E on UV such that UV gets split on a 3 : 4 ratio from U to V, keeping in mind that U(2 , -4) and V(4 ,3)
[tex]\textit{internal division of a line segment using ratios} \\\\\\ U(2,-4)\qquad V(4,3)\qquad \qquad \stackrel{\textit{ratio from U to V}}{3:4} \\\\\\ \cfrac{U\underline{E}}{\underline{E} V} = \cfrac{3}{4}\implies \cfrac{U}{V} = \cfrac{3}{4}\implies 4U=3V\implies 4(2,-4)=3(4,3)[/tex]
[tex](\stackrel{x}{8}~~,~~ \stackrel{y}{-16})=(\stackrel{x}{12}~~,~~ \stackrel{y}{9})\implies E=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{8 +12}}{3+4}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-16 +9}}{3+4} \right)} \\\\\\ E=\left( \cfrac{20}{7}~~,~~\cfrac{-7}{7} \right)\implies E=\left( 2\frac{6}{7}~~,~~-1 \right)[/tex]
