The rotation about (0,0) through angle G has three properties: (0, 0) is mapped into itself. The distance from (x,y) to (0, 0) is the same as the distance form Q(x,y) to (0, 0). The angle formed by the rays from (0,0) to (x,y) and to (x',y') is the same as the angle formed by the rays from (0,0) to Q(x,y) and to Q(x',y'). Show those three things.

For example, it is easy to show that x'= 0(cos G)- 0(sin G)= 0 and y'= 0(sin G)+ 0(cos G)= 0.

The distance from (0, 0) to Q(x, y) is