[tex]\bf \textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{10}~,~\stackrel{y_2}{8})~\hspace{8em} \frac{1}{4}\textit{ of the way from }A\to B \\\\[-0.35em] ~\dotfill\\\\ \stackrel{~\hfill \textit{component form of segment AB}}{ (\stackrel{x_2}{10}-\stackrel{x_1}{2}, \stackrel{y_2}{8}-\stackrel{y_1}{4})\qquad \implies \qquad (8,4)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{~\hfill \textit{values to be added to Point A coordinates}} {\cfrac{1}{4}(8,4)\implies \cfrac{1}{4}(8)~,~\cfrac{1}{4}(4)\qquad \implies \qquad \left(2,1\right)} \\\\\\ \stackrel{\textit{addition of Point A coordinates and values}} {(2,4)+\left( 2,1\right)\qquad \implies \blacktriangleright \left( 4,5\right) \blacktriangleleft }[/tex]
