If a line joining two points A ( 2, 0) and B ( 3, 1) is rotated about A in anticlockwise direction through an angle 15° such that the point B goes to C in the new position, then the coordinates of C are

The equation of AC isx−2cos⁡60∘=y−0sin⁡60∘=rWe have, AB=(3−2)2+(1−0)2=2As ACis the new position of AB. Therefore, AC=AB=2.Thus, the coordinates of C are given by   x−2cos⁡60∘=y−0sin⁡60∘=2⇒x=2+12,y=32Hence, the coordinates of C are 2+12,32.