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9) Suppose a coordinate system Sis rotated about its origin by angle op to become a new coordinate system s', as shown in the following figure. A point in a plane has coordinates (x,y) in S and coordinates (x,y)in S. (a) Show that, during the transformation of rotation, the coordinates in S' are expressed in terms of the coordinates in S by the following relations: x' = x cos 0 + y sin y' = -xsin + y coso (b) Show that the distance of point P to the origin is invariant under rotations of the coordinate system. In other words, show that Vx² + y² = (x² + y2