If the line joining two points $\mathrm{A}(2,0)$ and $\mathrm{B}(3,1)$ is rotated about $\mathrm{A}$ in anticlockwise direction through an angle of $15^{\circ}$, then the equation of the line in new position is

• A

  $y=3 x-6$
• Correct answer
  B

  $y=\sqrt{3} x-2 \sqrt{3}$
• C

  $y=-\sqrt{3} x+2 \sqrt{3}$
• D

  $y=\frac{1}{\sqrt{3}} x-\frac{2}{\sqrt{3}}$

Solution

Refer Figure
Slope of $\mathrm{AB}=\frac{1-0}{3-2}=1$ $$ \therefore \tan \theta=1 \Rightarrow \theta=45^{\circ} $$ Line $\mathrm{AB}$ is rotated through $15^{\circ}$ in anticlockwise direction about A. Therefore in a new position, slope of line $=\tan \left(45^{\circ}+15^{\circ}\right)=\tan 60^{\circ}=\sqrt{3}$ and it passes through $\mathrm{A}$. Required equation of line is $(\mathrm{y}-0)=\sqrt{3}(\mathrm{x}-2) \Rightarrow$ $$ \sqrt{3} x-2 \sqrt{3}=y $$

Hence, the correct answer is option: 'B'.