Question

Find the coordinates of P so that P partitions AB in the ratio 1 to 3 with A (2,-6) and B (6,6)

Answer 1

`\textit{internal division of a line segment using ratios} \\\\\\ A(2,-6)\qquad B(6,6)\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(2,-6)=1(6,6)`

`(\stackrel{x}{6}~~,~~ \stackrel{y}{-18})=(\stackrel{x}{6}~~,~~ \stackrel{y}{6})\implies P=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{6+6}}{1+3}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-18+6}}{1+3} \right)} \\\\\\ P=\left( \cfrac{12}{4}~~,~~\cfrac{-12}{4} \right)\implies P=(3~~,~~-3)`