Question

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

Answer 1

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

thus the angle made with the axis is ${45}^o$

Let after rotation the $P+B$ reaches to the $P+C$

Such that $\angle CAB={15}^o$

Thus the slope of the line $CA$ be $\tan (45-{15}^o)=\tan {60}^o=\sqrt{3}$

coordinate of the pt $A$ are $(2,0)$ therefore the equation of the line $CA$ is

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

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