Question

If the acute angle between two line 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 between the lines with slpe $m_1$ and $m_2$,

Then $tan\theta =\left|\frac{m_1-m_2}{1+m_1{m}_2}\right|$

If $\theta =\frac{\pi }{4}$ and $m_1=\frac{1}{2}$

$tan\frac{\pi }{4}=\left|\frac{\frac{1}{2}-m_2}{1+\frac{1}{2}{m}_2}\right|$

$1=\left|\frac{1-2m_2}{2+m_2}\right|$

$\frac{1-2m_2}{2+m_2}=1or\frac{1-2m_2}{2+m_2}=-1$

$1-2m_2=2+m_2$ $1-2m_2=-2-m_2$

$-1=3m_2$ $m_2=3$

$m_2=\frac{-1}{3}$

So,slope of the other line is either $-\frac{1}{3}or3$