Question

The point B lies on the segment AC find coordinates of B so that AB is 1/5 of AC. A (-22,25) C (3,-5)

Answer 1

now, we're assuming 1/5 from A to C, so in essence 1/5 from A

`\textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{-22}~,~\stackrel{y_1}{25})\qquad C(\stackrel{x_2}{3}~,~\stackrel{y_2}{-5})~\hspace{8em} (1)/(5)\textit{ of the way from A to C} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_2}{3}-\stackrel{x_1}{(-22)}~~,~~ \stackrel{y_2}{-5}-\stackrel{y_1}{25})\qquad \implies \qquad \stackrel{\stackrel{\textit{\small component form of}}{\textit{\small segment AC}}}{\left( 25 ~~,~~ -30 \right)} \\\\[-0.35em] ~\dotfill`

`\left( \stackrel{x_1}{-22}~~+~~(1)/(5)(25)~~,~~\stackrel{y_1}{25}~~+~~(1)/(5)(-30) \right)\implies (-22+5~~,~~25-6) \\\\\\ ~\hfill~B=(-17~~,~~19)~\hfill~`