Question

Find the angle formed by the lines 2x + y - 8 = 0 and x + 3y + 4 = 0

• A. 30${}^{\circ }$
• B. 35${}^{\circ }$
• C. 45${}^{\circ }$
• D. 60${}^{\circ }$
• E. none of these

Answer 1

Answer: (C)

45${}^{\circ }$

Let $m_1,m_2$ be slopes of lines $y=-2x+8=0$ and $y=-\frac{1}{3}x-\frac{4}{3}=0$
$\Rightarrow m_1=-2,m_2=-\frac{1}{3}$
Let $\theta$ be angle between the given lines.
$\Rightarrow tan\theta =|\frac{m_1-m_2}{1+m_1{m}_2}|$
$=|\frac{-2+\frac{1}{3}}{1+(-2)(-\frac{1}{3})}|$
$=|\frac{-\frac{5}{3}}{\frac{5}{3}}|$
$\Rightarrow tan\theta =1$
$\Rightarrow \theta ={45}^0$
Option C is correct.