Question

Please give me a correct answer and the step by step explanation.

Answer 1

keeping in mind that the points are A(-8 , 6) and C(2 , 5), so

`\textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{-8}~,~\stackrel{y_1}{6})\qquad C(\stackrel{x_2}{2}~,~\stackrel{y_2}{5})~\hspace{8em} (2)/(5)\textit{ of the way from A to C} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_2}{2}-\stackrel{x_1}{(-8)}~~,~~ \stackrel{y_2}{5}-\stackrel{y_1}{6})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AC}}}{\left( 10 ~~,~~ -1 \right)} \\\\[-0.35em] ~\dotfill`

`\left( \stackrel{x_1}{-8}~~+~~(2)/(5)(10)~~,~~\stackrel{y_1}{6}~~+~~(2)/(5)(-1) \right)\implies \left(-8+4~~,~~6-(2)/(5) \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill B\left(-4~~,~~5(3)/(5) \right)~\hfill`