The line joining the points A (2,0) and B(3, 1) is rotated through an angle of 45⁰, about A in the anticlockwise direction. The coordinates of B in the position

Given A (2, 0)  B (3, 1)

Slope of AB = 1-0/3-2 = 1

Angle made by the line AB with x-axis = 45⁰

Let  $\theta =$ Angle made by AC with x-axis $={45}^0+{45}^0={90}^0$

 $\begin{array}{l}A\left(2,0\right)=\left(x_1,y_1\right),\theta ={90}^0\\ r=AB=\sqrt{1^2+1^2}=\sqrt{2}\\ \therefore C=\left(x_1+r\cos \theta ,y_1+r\sin \theta \right)=\left(2+\sqrt{2}\cos {90}^0,0+\sqrt{2}\sin {90}^0\right)\\ =\left(2+0,0+\sqrt{2}\right)\\ =\left(2,\sqrt{2}\right)\end{array}$