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Talja [164]
3 years ago
13

Point C with coordinates (-3.6, -3.4) divides in the ratio 2 : 3. If A = (-2, -1), what are the coordinates of point B

Mathematics
1 answer:
juin [17]3 years ago
8 0
\bf \left. \qquad  \right.\textit{internal division of a line segment}
\\\\\\
A(-2,-1)\qquad B(x,y)\qquad
\qquad 2:3
\\\\\\
\cfrac{AC}{CB} = \cfrac{2}{3}\implies \cfrac{A}{B} = \cfrac{2}{3}\implies 3A=2B\implies 3(-2,-1)=2(x,y)\\\\
-------------------------------\\\\
{ C=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}\\\\
-------------------------------

\bf C=\left(\cfrac{(3\cdot -2)+(2\cdot x)}{2+3}\quad ,\quad \cfrac{(3\cdot -1)+(2\cdot y)}{2+3}\right)~~=~~(-3.6~~,~~-3.4)
\\\\\\
C=\left(\cfrac{-6+2x}{5}~~,~~\cfrac{-3+2y}{5}  \right)~~~=~~~(-3.6~~,~~-3.4)\\\\
-------------------------------\\\\
\cfrac{-6+2x}{5}=-3.6\implies -6+2x=-18\implies 2x=-12
\\\\\\
x=\cfrac{-12}{2}\implies \boxed{x=-6}\\\\
-------------------------------\\\\
\cfrac{-3+2y}{5} =-3.4\implies -3+2y=-17
\\\\\\
2y=-14\implies y=\cfrac{-14}{2}\implies \boxed{y=-7}
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