0 e = -(6), -(i). P=(-2). = -(33). 0 Let a) Find an orientation-preserving isometry for m: R2 R so that m(e)=p, m (e) = q Express m in the form m (x) = 4x + v where A is an orthogonal 22 matrix and v E R. Explain why m is a rotation and determine the angle and centre of rotation. Hint: Consider m (e) - m (e) b) Find an orientation-reversing isometry for m': R R so that m'(e) = p , m' () = q Express m in the form m'(x) = A'x+v where A' is an orthogonal 22 matrix and v E R. Explain why m' is a glide reflection and determine mirror line and translation vector. c) Explain why m and m' are unambiguously determined. q= 0 e = -(6), -(i). P=(-2). = -(33). 0 Let a) Find an orientation-preserving isometry for m: R2 R so that m(e)=p, m (e) = q Express m in the form m (x) = 4x + v where A is an orthogonal 22 matrix and v E R. Explain why m is a rotation and determine the angle and centre of rotation. Hint: Consider m (e) - m (e) b) Find an orientation-reversing isometry for m': R R so that m'(e) = p , m' () = q Express m in the form m'(x) = A'x+v where A' is an orthogonal 22 matrix and v E R. Explain why m' is a glide reflection and determine mirror line and translation vector. c) Explain why m and m' are unambiguously determined. q=