Question

Given the points r(8, -2) and (-7, -7), find the coordinates of point s on ri such that the ratio of r$ to st is 3:2.

Answer 1

`\textit{internal division of a line segment using ratios} \\\\\\ R(8,-2)\qquad T(-7,-7)\qquad \qquad \stackrel{\textit{ratio from R to T}}{3:2} \\\\\\ \cfrac{R\underline{S}}{\underline{S} T} = \cfrac{3}{2}\implies \cfrac{R}{T} = \cfrac{3}{2}\implies 2R=3T\implies 2(8,-2)=3(-7,-7)`

`(\stackrel{x}{16}~~,~~ \stackrel{y}{-4})=(\stackrel{x}{-21}~~,~~ \stackrel{y}{-21})\implies S=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{16 -21}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-4 -21}}{3+2} \right)} \\\\\\ S=\left( \cfrac{-5}{5}~~,~~\cfrac{-25}{5} \right)\implies S=(-1~~,~~-5)`