Thank you for reporting, we will resolve it shortly
Q.
If the angle between two lines is $\frac{\pi}{4}$ and slope of the lines is $\frac{1}{2}$, then which of the following is not the slope of the other line?
Straight Lines
Solution:
We know that, the acute angle $\theta$ between two lines with slopes $m_1$ and $m_2$ is given by
$\tan \theta=\left|\frac{m_2-m_1}{1+m_1 m_2}\right|.......$(i)
Let $ m_1=\frac{1}{2}, m_2=m$ and $\theta=\frac{\pi}{4}$
Now, putting these values in Eq. (i), we get
$\tan \frac{\pi}{4} =\left|\frac{m-\frac{1}{2}}{1+\frac{1}{2} m}\right| $
$1 =\left|\frac{m-\frac{1}{2}}{1+\frac{1}{2} m}\right|$
which gives $\frac{m-\frac{1}{2}}{1+\frac{1}{2} m}=1$
or $\frac{m-\frac{1}{2}}{1+\frac{1}{2} m}=-1$
Therefore, $m=3$ or $m=-\frac{1}{3}$
Hence, slope of the other line is 3 or $-\frac{1}{3}$.
