Question

On a coordinate plane, point A is located at (-1, -3) and point B is located at (5, -4). Determine the coordinates of the point that

is 8/9 of the distance from A to B. Write in the form (x,y).

Answer 1

`\textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-3})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{-4})~\hspace{8em} (8)/(9)\textit{ of the way from A to B} \\\\[-0.35em] ~\dotfill`

`(\stackrel{x_2}{5}-\stackrel{x_1}{(-1)}~~,~~ \stackrel{y_2}{-4}-\stackrel{y_1}{(-3)})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AB}}}{\left( 6 ~~,~~ -1 \right)} \\\\[-0.35em] ~\dotfill\\\\ \left( \stackrel{x_1}{-1}~~+~~(8)/(9)(6)~~,~~\stackrel{y_1}{-3}~~+~~(8)/(9)(-1) \right)\implies \left( \cfrac{13}{3}~~,~~-\cfrac{35}{9} \right)`