Let f : R 2 → R 2 be the rigid motion defined by f (a, b) = 1 √ 2 (2 − a + b, 1 + a + b). Express f in the form f = g ◦

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Let f : R 2 → R 2 be the rigid motion defined by f (a, b) = 1 √2 (2 − a + b, 1 + a + b). Express f in the form f = g ◦ T where gis a translation and T an orthogonal operator on R 2 . Find thevector v0 by which g translates. If T is a rotation, find the angleθ through which it rotates. If T is a reflection about a line Lthrough the origin, find the angle α that L makes with the positivex-axis.