Answer:
Let point \[P\left( \frac{3}{4},\frac{5}{12} \right)\] divides the line AB in ratio \[k:1\] Then, by section formula, coordinates of P are \[\frac{2k+\frac{1}{2}}{k+1}=\frac{3}{4}\] and \[\frac{-5k+\frac{3}{2}}{k+1}=\frac{5}{12}\] \[\Rightarrow 8k+2=3k+3\] and \[-60k+18=5k+5\] \[\Rightarrow 8k-3k=3-2\] and \[65k=18-5\] \[\Rightarrow 5k=1\] and \[65k=13\Rightarrow k=\frac{1}{5}\]in each case Hence the required ratio is \[1:5\].
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