Question

What angle does the line segment joining $(5,2)$ and $(6,-15)$ subtend at $(0,0)$?

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{2}$
• D. $\frac{3\pi }{4}$

Answer 1

The correct option is C $\frac{\pi }{2}$

Given $2$ points are $(5,2),(6,-15)$

Slope of the line joining first point to the origin is $m_1=\frac{2-0}{5-0}=\frac{2}{5}$

Slope of the line joining second point to the origin is $m_2=\frac{-15-0}{6-0}=\frac{-5}{2}$

Let the angle subtended by these two points at $(0,0)$ is $\theta$

$\therefore \tan \theta =\frac{m_1-m_2}{1+m_1{m}_2}=\frac{\frac{2}{5}-(-\frac{5}{2})}{1+(\frac{2}{5}\times -\frac{5}{2})}=\frac{\left(\frac{29}{10}\right)}{\left(0\right)}=\infty$

$\therefore \theta =ta{n}^{-1}\infty ={90}^o=\frac{\pi }{2}$

Hence, option C is correct.