(17 marks in total) Consider the map F : E2 > E2 given by (way)'>(%wy++1\\2[w+y 3+2)- 2.1. Show that F is an isometry of E2, (5 marks). 2.2. Find the unique xed point (3:0, yo) of F, that is the unique point (3:0, yo) 6 E2 such that F(a:0,y0) = (350,310), (5 marks). 2.3 Show that F is a rotation centered at the point (3:0, yo) obtained in 2.2 by express ing it as F : T o R o T'1 , where T : E2 > E2 is the translation (any) I> (350,310) and R : E2 > E2 is the counterclockwise rotation of center (0, 0) by an angle g, (7 marks)