The line joining two points A (2, 0), B( 3, 1) is rotated about A in anti clock wise direction through an angle 15⁰. If B goes to C then C=

Given A (2, 0) B ( 3, 1)

Slope of $AB\text{\hspace{0.17em}}=\frac{1-0}{3-2}=1$

Angle made by the line AB with X- axis is $\frac{\pi }{4}$

 $\begin{array}{l}\therefore \theta =Anglemadebytheline\overline{AC}withX-axis\\ =\theta ={45}^0+{15}^0={60}^0\\ r=AC=AB=\sqrt{{\left(3-2\right)}^2+{\left(1-0\right)}^2}=\sqrt{1+1}=\sqrt{2}\\ \therefore C=\left(x_1+r\cos \theta y_1+r\sin \theta \right)\\ =\left(2+\sqrt{2}\cos {60}^{0}0+\sqrt{2}\sin {60}^0\right)\\ =\left(2+\sqrt{2}\left(\frac{1}{2}\right)\sqrt{2}\left(\frac{\sqrt{3}}{2}\right)\right)\\ =\left(2+\frac{1}{\sqrt{2}},\sqrt{\frac{3}{2}}\right)\end{array}$