A line joining two points A(2, 0) and B(3, 1) is rotated about A in anticlockwise direction through an angle 15∘. If B goes to C in the new position, then the coordinates of C are
Slope of line
AB=0−12−3=1=tan 45∘∴ ∠BAX=45∘
Given ∠CAB=15∘∴ ∠CAX=60∘∴ Slope of the AC=tan 60∘=√3
Now, line AC makes an angle of 60∘ with positive direction of x-axis and
AC=AB=√(3−2)2+(1−0)2=√2
∴ Coordinates of C are 2+√2 cos 60∘,0+√2sin 60∘
i.e. (2+1√2,√32)