Question

Find the coordinates

Answer 1

`\textit{internal division of a line segment using ratios} \\\\\\ A(-3,2)\qquad B(5,5)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:3} \\\\\\ \cfrac{A\underline{P}}{\underline{P} B} = \cfrac{1}{3}\implies \cfrac{A}{B} = \cfrac{1}{3}\implies 3A=1B\implies 3(-3,2)=1(5,5)`

`(\stackrel{x}{-9}~~,~~ \stackrel{y}{6})=(\stackrel{x}{5}~~,~~ \stackrel{y}{5}) \implies P=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-9 +5}}{1+3}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{6 +5}}{1+3} \right)} \\\\\\ P=\left( \cfrac{ -4 }{ 4 }~~,~~\cfrac{ 11}{ 4 } \right)\implies {\Large \begin{array}{llll} P=(-1~~,~~2.75) \end{array}}`