rotate and translate the coordinate system until the isometry looks like hˉ(z)= zˉ +a, with a real, which is a glide reflection along thex-axis. 7.3.5. Show that if z ′=(cosϕ+isinϕ)z is taken as the new coordinate of the point z, then the x - and y-axes of this new coordinate system are the result of rotating the x and y-axes through −ϕ. Now suppose that f(z)=(cosθ+isinθ)z+d is an orientation-reversing isometry. Thus, in the old coordinate system, the isometry sends z to (cosθ+isinθ)Σ+d
