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Find the ratio in which the point P(2,1)divide the line segment joining the points A(1,-2) and B(4,7).

Let the ratio be a:1

Hence the point of dividing is

\left({\frac  {4a+7}{a+1}},{\frac  {7a-2}{a+1}}\right)=(2,1)\,

Now comparing both sides,we get

{\frac  {4a+1}{a+1}}=2,{\frac  {7a-2}{a+1}}=1\,


a={\frac  {1}{2}},a={\frac  {1}{2}}\,

Hence the ratio is 1:2

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