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Question Number 75300 by vishalbhardwaj last updated on 09/Dec/19

$$\mathrm{A}\mathrm{line}\mathrm{is}\mathrm{such}\mathrm{that}\mathrm{its}\mathrm{segment}\mathrm{between}$$$$\mathrm{the}\mathrm{lines}5\mathrm{x}-\mathrm{y}+4=0\mathrm{and}3\mathrm{x}+4\mathrm{y}-4=0$$$$\mathrm{is}\mathrm{bisected}\mathrm{at}\mathrm{the}\mathrm{point}(1,5).\mathrm{Obtain}\mathrm{its}$$$$\mathrm{equation}?$$

Answered by mr W last updated on 09/Dec/19

$$saytheeqn.is$$$$\frac{y-5}{x-1}=m$$$$\Rightarrow y=mx+5-m$$$$5x-mx-5+m+4=0$$$$\Rightarrow x=\frac{1-m}{5-m}$$$$3x+4mx+20-4m-4=0$$$$\Rightarrow x=\frac{4m-16}{3+4m}$$$$\frac{1}{2}(\frac{1-m}{5-m}+\frac{4m-16}{3+4m})=1$$$$\Rightarrow m=\frac{107}{3}$$$$\frac{y-5}{x-1}=\frac{107}{3}$$$$\Rightarrow 107x-3y-92=0$$

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