L-1-and-L-2-are-two-lines-which-intersects-each-other-at-a-right-angle-at-the-point-1-3-L-1-cuts-the-y-axis-at-the-point-0-2-find-the-equations-of-L-1-and-L-2-

Question Number 47821 by mondodotto@gmail.com last updated on 15/Nov/18

$$\boldsymbol{\mathrm{L}}_{\mathrm{1}} \boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{L}}_{\mathrm{2}} \:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{two}}\:\boldsymbol{\mathrm{lines}}\:\boldsymbol{\mathrm{which}}\:\boldsymbol{\mathrm{intersects}} \\ $$$$\boldsymbol{\mathrm{each}}\:\boldsymbol{\mathrm{other}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{right}}\:\boldsymbol{\mathrm{angle}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{point}}\:\left(\mathrm{1},\mathrm{3}\right),\boldsymbol{\mathrm{L}}_{\mathrm{1}} \:\boldsymbol{\mathrm{cuts}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{y}}−\boldsymbol{\mathrm{axis}}\:\boldsymbol{\mathrm{at}} \\ $$$$\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{point}}\:\left(\mathrm{0},\mathrm{2}\right)\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{equations}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{L}}_{\mathrm{1}} \boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{L}}_{\mathrm{2}} \\ $$$$ \\ $$

Answered by tanmay.chaudhury50@gmail.com last updated on 15/Nov/18

$${eqn}\:{L}_{\mathrm{1}} \:\:{y}−\mathrm{3}=\frac{\mathrm{2}−\mathrm{3}}{\mathrm{0}−\mathrm{1}}\left({x}−\mathrm{1}\right) \\ $$$${y}−\mathrm{3}=\left({x}−\mathrm{1}\right)\:\:\:{y}−{x}−\mathrm{2}=\mathrm{0} \\ $$$${slope}\:{L}_{\mathrm{1}} =\mathrm{1}\:\:\:{slope}\:{L}_{\mathrm{2}} =−\mathrm{1}\:\:\left[{m}_{\mathrm{1}} {m}_{\mathrm{2}} =−\mathrm{1}\right] \\ $$$${eqn}\:{L}_{\mathrm{2}} \:{y}−\mathrm{3}=\left(−\mathrm{1}\right)\left({x}−\mathrm{1}\right) \\ $$$${y}−\mathrm{3}=−{x}+\mathrm{1} \\ $$$${y}+{x}−\mathrm{4}=\mathrm{0} \\ $$$$\:\: \\ $$

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