Question

The angle made by the line joining the points $(2,0)$ and $(-4,2\sqrt{3})$ with x axis is -

• A. ${120}^0$
• B. ${60}^0$
• C. ${150}^0$
• D. ${135}^0$

Answer 1

The correct option is C ${150}^0$

Angle made by the line joining the points

$\left(2,0\right)and\left(-4,2\sqrt{3}\right)$ with $x$ axis.

Slope of line

$m=\frac{\Delta y}{\Delta x}$

$=\frac{y_2-y_1}{x_2-x_1}=\frac{2\sqrt{3}-0}{-4-2}$

$=\frac{2\sqrt{3}}{-6}=\frac{\sqrt{3}}{-\sqrt{3}\times \sqrt{3}}=\frac{-1}{\sqrt{3}}$

$m=\tan \theta$

$\tan \theta =\frac{-1}{\sqrt{3}}$

$\theta =-{\tan }^{-1}\frac{1}{\sqrt{3}}={150}^{\circ }.$