Distance AB=√(√3)2+12=2 units
The slope of the line AB is given by
m=1−02+√3−2=1√3
⇒tanθ=1√3⇒θ=π6
∴ The line makes on angle of 30∘ with x−axis.
AB is rotated through 30∘about point A in anticlock wise. So, it makes an angle of 60∘ with x−axis.
The new coordinates of B is
(2+ABcosθ,0+ABsinθ)=(2+2cos60∘,2sin60∘)=(3,√3)∴h2+k2=9+3=12