Question

The line joining two points $A(2,0),B(3,1)$ is rotated about $A$ in anticlockwise direction through an angle of ${15}^o$. Find the equation of the line in the new position. If $B$ goes to $C$ in the new position, what will be the co-ordinates of $C$, in the new position?

Answer 1

$A$ is $(2,0)$, $B$ or $(3,1)$
Also $AB\sqrt{2}$.
Slope of $AB=(1-0)/(3-2)=1=\tan \theta$
$\therefore \theta ={45}^o$
Now $AB$ is rotated through ${15}^o$ in anti-clock wise direction and hence it makes an angle of ${60}^o$ with $x-$axis. Since it passes through $(2,0)$ its equation in new position is
$\frac{x-2}{\cos {60}^o}=\frac{y-0}{\sin {60}^o}=r=AC=AB\sqrt{2}$
Hence the coordinate of $C$ are
$2+\sqrt{2}\cos {60}^o,0+\sqrt{2}\sin {60}^o$
or $\left[\right(4+\sqrt{2})/2,\sqrt{6}/2]$