Question

If S is (7,2) and T is (1,-5) what is 1/6 of that line

Answer 1

`\textit{internal division of a segment using a fraction}\\\\ S(\stackrel{x_1}{7}~,~\stackrel{y_1}{2})\qquad T(\stackrel{x_2}{1}~,~\stackrel{y_2}{-5})~\hspace{8em} (1)/(6)\textit{ of the way from S to T} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_2}{1}-\stackrel{x_1}{7}~~,~~ \stackrel{y_2}{-5}-\stackrel{y_1}{2})\qquad \implies \qquad \stackrel{\stackrel{\textit{\small component form of}}{\textit{\small segment ST}}}{\left( -6 ~~,~~ -7 \right)} \\\\[-0.35em] ~\dotfill`

`\left( \stackrel{x_1}{7}~~+~~(1)/(6)(-6)~~,~~\stackrel{y_1}{2}~~+~~(1)/(6)(-7) \right)\implies \left( 7-1~~,~~2-(7)/(6) \right) \\\\\\ ~\hfill~ {\Large \begin{array}{llll} \left(6~~,~~(5)/(6) \right) \end{array}}~\hfill~`