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nordsb [41]
2 years ago
6

Find the coordinats of P

Mathematics
1 answer:
Crazy boy [7]2 years ago
5 0

\textit{internal division of a line segment using ratios} \\\\\\ A(8,6)\qquad B(-2,-9)\qquad \qquad \stackrel{\textit{ratio from A to B}}{3:2} \\\\\\ \cfrac{A\underline{P}}{\underline{P} B} = \cfrac{3}{2}\implies \cfrac{A}{B} = \cfrac{3}{2}\implies 2A=3B\implies 2(8,6)=3(-2,-9)

(\stackrel{x}{16}~~,~~ \stackrel{y}{12})=(\stackrel{x}{-6}~~,~~ \stackrel{y}{-27})\implies P=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{16-6}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{12-27}}{3+2} \right)} \\\\\\ P=\left( \cfrac{10}{5}~~,~~\cfrac{-15}{5} \right)\implies P=(2~~,~~-3)

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