![]() ![]() It is the only isometry which belongs to more than one of the types described above. The identity isometry, defined by I( p) = p for all points p is a special case of a translation, and also a special case of a rotation. This is a glide reflection, except in the special case that the translation is perpendicular to the line of reflection, in which case the combination is itself just a reflection in a parallel line. That is, we obtain the same result if we do the translation and the reflection in the opposite order.)Īlternatively we multiply by an orthogonal matrix with determinant −1 (corresponding to a reflection in a line through the origin), followed by a translation. Neither are less drastic alterations like bending, stretching, or twisting.Īn isometry of the Euclidean plane is a distance-preserving transformation of the plane. ![]() However, folding, cutting, or melting the sheet are not considered isometries. There is one further type of isometry, called a glide reflection (see below under classification of Euclidean plane isometries). These are examples of translations, rotations, and reflections respectively. Notice that if a picture is drawn on one side of the sheet, then after turning the sheet over, we see the mirror image of the picture.
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