Question

The line joining two points $A(2,0);B(3,1)$ is rotated about $A$ in the anticlockwise direction through an angle of ${15}^o$. The equation of the line in the new position is :

• A. $x-\sqrt{3y}-2=0$
• B. $x-2y-2=0$
• C. $\sqrt{3x}-y-2\sqrt{3}=0$
• D. none

Answer 1

The correct option is C $\sqrt{3x}-y-2\sqrt{3}=0$

The slope of the line $AB$ $=\frac{1-0}{3-2}=1$

Thus the angle made with the $x-axis$ is ${45}^{\circ }$ ;eft after rotation The point $B$ reaches to the point $C$ such that $\angle CAB=15$

thus the slope of line $CB$ be $\tan (45+15)=\tan {60}^{\circ }=\sqrt{3}$

so, coordinates of the point $A$ are $(2,0)$

The equation of the line $CA$ is :

$y-0=\sqrt{3}(x-2)$

$\to \sqrt{3}x-y-2\sqrt{3}=0$