Aspire Faculty ID #11993 · Topic: NIMCET 2025 · Just now
NIMCET 2025

The obtuse angle between lines 2y = x + 1 and y = 3x + 2 is

Solution

Given lines: 
$2y = x + 1$ and $y = 3x + 2$. 
 From $2y = x + 1$ 
we get $y = \dfrac{1}{2}x + \dfrac{1}{2}$, 
so slope $m_1 = \dfrac{1}{2}$. 

 From $y = 3x + 2$, 
 slope $m_2 = 3$. 

 Angle between two lines: $ \tan\theta = \left|\dfrac{m_2 - m_1}{1 + m_1 m_2}\right| $ 
 $ \tan\theta = \left|\dfrac{3 - \dfrac{1}{2}}{1 + \dfrac{1}{2}\cdot 3}\right| = \dfrac{\dfrac{5}{2}}{\dfrac{5}{2}} = 1 $ 
So $\theta = 45^\circ$ or $135^\circ$. 
Required obtuse angle $= 135^\circ$.
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