Then a rotation can be represented as a matrix, Let these rotations and reflections operate on all points on the plane, and let these points be represented by position vectors. Let a reflection about a line L through the origin which makes an angle θ with the x-axis be denoted as Ref( θ). Let a rotation about the origin O by an angle θ be denoted as Rot( θ). The statements above can be expressed more mathematically. On the other hand, the composition of a reflection and a rotation, or of a rotation and a reflection (composition is not commutative), will be equivalent to a reflection. I.e., angle ∠ POP′′ will measure 2 θ.Ī pair of rotations about the same point O will be equivalent to another rotation about point O. If lines L 1 and L 2 make an angle θ with one another, then points P and P′′ will make an angle 2 θ around point O, the intersection of L 1 and L 2. Then reflect P′ to its image P′′ on the other side of line L 2. First reflect a point P to its image P′ on the other side of line L 1. In Euclidean geometry, two-dimensional rotations and reflections are two kinds of Euclidean plane isometries which are related to one another.Ī rotation in the plane can be formed by composing a pair of reflections.
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