Question

Please show work if any

Answer 1

looking at the picture above, we can see the points are

A(-2 , -8) and B(4 , 7), so

`\textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-8})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{7})~\hspace{8em} (2)/(3)\textit{ of the way from A to B} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_2}{4}-\stackrel{x_1}{(-2)}~~,~~ \stackrel{y_2}{7}-\stackrel{y_1}{(-8)})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AB}}}{\left( 6 ~~,~~ 15 \right)} \\\\[-0.35em] ~\dotfill`

`\left( \stackrel{x_1}{-2}~~+~~(2)/(3)(6)~~,~~\stackrel{y_1}{-8}~~+~~(2)/(3)(15) \right)\implies (-2+4~~,~~-8+10) \\\\\\ ~\hfill~ {\Large \begin{array}{llll} \stackrel{ F }{(2~~,~~2)} \end{array}}~\hfill~`