Question

The slope of a line that makes an angle of measure${30}^{\circ }$ with positive direction of $y$-axis measured anticlockwise is

• A. $\sqrt{3}$
• B. $-\sqrt{3}$
• C. $\frac{1}{\sqrt{3}}$
• D. none of these

Answer 1

The correct option is B

$-\sqrt{3}$

Explanation for the correct option:

Find the slope of the given line.

Given: the line makes angle ${30}^{\circ }$ with positive direction of $y$-axis.

So the angle made by line with $x$-axis will be ${90}^{\circ }+{30}^{\circ }={120}^{\circ }$

Thus, the slope of the given line $=\tan \theta$

$$\begin{gathered} =\tan {120}^{\circ } \\ =–\tan {60}^{\circ } \\ =-\sqrt{3} \end{gathered}$$

Hence, option $B$ is the correct answer.