Question

If the acute angle between two lines is $\frac{\pi }{4}$ and slope of one of them is $\frac{1}{2}$. Find the slope of the other line.

• A. 2
• B.
• C. 3
• D.

Answer 1

Answer: (C), (D)

The correct options are
C

3

D

If $\theta$ be the angle between the lines with slope m_1 and m_2,
Then $tan\theta =|\frac{m_1-m_2}{1+m_1{m}_2}|$

If $\theta =\frac{\pi }{4}and{m}_1=1$
$tan\frac{\pi }{4}=|\frac{\frac{1}{2}-m_2}{1+\frac{1}{2}{m}_2}|$
$1=|\frac{1-2m_2}{2+m_2}|$
$\frac{1-2m_2}{2+m_2}=1or\frac{1-2m_2}{2+m_2}=-1$

$1-2m_2=2+m_{2}1-2m_2=-2-m_2$
$-1=3m_2{m}_2=3$
$m_2=\frac{-1}{3}$
So, slope of the other line is either $\frac{-1}{3}$ or 3.