Question

Point X on line AB is 1/5 of distance from A to B A=(-5,-5) B=(2,9)

Answer 1

`\textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{-5}~,~\stackrel{y_1}{-5})\qquad B(\stackrel{x_2}{2}~,~\stackrel{y_2}{9})~\hspace{8em} (1)/(5)\textit{ of the way from A to B} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_2}{2}-\stackrel{x_1}{(-5)}~~,~~ \stackrel{y_2}{9}-\stackrel{y_1}{(-5)})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AB}}}{\left( 7 ~~,~~ 14 \right)} \\\\[-0.35em] ~\dotfill`
`\left( \stackrel{x_1}{-5}~~+~~(1)/(5)(7)~~,~~\stackrel{y_1}{-5}~~+~~(1)/(5)(14) \right) \implies \left(-\cfrac{18}{5}~~,~-\cfrac{11}{5} \right) \\\\\\ ~\hfill~ {\Large \begin{array}{llll} \left(-3(3)/(5)~~,~-2(1)/(5) \right) \end{array}}~\hfill~`