The slope of the line through the origin which makes an angle of $30^{\circ}$ with the positive direction of…

The slope of the line through the origin which makes an angle of $30^{\circ}$ with the positive direction of $\mathrm{Y}$-axis measured anticlockwise is
  1. $\frac{-2}{\sqrt{3}}$
  2. $-\sqrt{3}$
  3. $\frac{\sqrt{3}}{2}$
  4. $\frac{-1}{\sqrt{3}}$

Solution

Refer figure Angle made by line $\mathrm{L}$ with positive direction of $\mathrm{X}$ axis is $\left(90^{\circ}+30^{\circ}\right)$ i.e. $120^{\circ}$. $\therefore$ Slope of line $\mathrm{L}=\tan \left(120^{\circ}\right)=\tan \left(\pi-60^{\circ}\right)=-\tan 60^{\circ}=-\sqrt{3}$

Asked in: MHT CET 2021 (20 Sep Shift 1)

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