If the angle between two lines is pi 4

Asked by admin @ 12/08/2021 in Math viewed by 356 People

If the angle between two lines pi/4 and slope of one of the lines is 1/2 , find the slope of the other line.

Answered by admin @ 12/08/2021

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

As we already know that :-

θ b/w two lines having slopes m1 and m2

Hence,

${\boxed{\sf\:{tan\theta=|\dfrac{m_{2}-m_{1}}{1+m_{1}m{2}}..... (1)}}}$

Assume,

${\boxed{\sf\:{m_{1}=\dfrac{1}{2}}}}$

${\boxed{\sf\:{m_{2}=m}}}$

${\boxed{\sf\:{\theta=\dfrac{\pi}{4}}}}$

$\textbf{\underline{Substituting\;value\;in\;(1)}}$

${\boxed{\sf\:{|\dfrac{m-1/2}{1+1/2m}|=\dfrac{\pi}{4}}}}$

${\boxed{\sf\:{|\dfrac{2m-1}{2+m}|=1}}}$

${\boxed{\sf\:{\dfrac{2m-1}{2+m}=\pm 1}}}$

${\boxed{\sf\:{\dfrac{2m-1}{2+m}=1}}}$

${\boxed{\sf\:{\dfrac{2m-1}{2+m}=-1}}}$

(2m - 1) = (2 + m)

(2m - 1) = (-2 - m)

m = 3

${\boxed{\sf\:{m=\dfrac{-1}{3}}}}$

Slope

${\boxed{\sf\:{3\;or\; \dfrac{-1}{3}}}}$

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