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Point Q is the reflection of point P through the line AB. In a plane (or, respectively, 3-dimensional) geometry, to find the reflection of a point drop a perpendicular from the point to the line (plane) used for reflection, and extend it the same distance on the other side. To find the reflection of a figure, reflect each point in the figure.
p2mm: TRHVG (translation, 180° rotation, horizontal line reflection, vertical line reflection, and glide reflection) Formally, a frieze group is a class of infinite discrete symmetry groups of patterns on a strip (infinitely wide rectangle), hence a class of groups of isometries of the plane, or of a strip.
The term horizontal (h) is used with respect to a vertical axis of rotation. In 2D, the symmetry group D n includes reflections in lines. When the 2D plane is embedded horizontally in a 3D space, such a reflection can either be viewed as the restriction to that plane of a reflection through a vertical plane, or as the restriction to the plane ...
One calls the vertical rays and semicircles the hyperbolic lines in HP. The geometry of points and hyperbolic lines in HP is an example of a non-Euclidean geometry; nevertheless, the construction of the line and distance concepts for HP relies heavily on the original geometry of Euclid.
A reflection in a line is an opposite isometry, like R 1 or R 2 on the image. Translation T is a direct isometry: a rigid motion. [1] In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.
In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2-dimensional space, there is a line/axis of symmetry, in 3-dimensional space, there is a plane of symmetry
D 1h and C 2v: group of order 4 with a reflection in a plane and a 180° rotation through a line in that plane; D 1d and C 2h: group of order 4 with a reflection in a plane and a 180° rotation through a line perpendicular to that plane. S 2 is the group of order 2 with a single inversion (C i). "Equal" is meant here as the same up to conjugacy ...
A rotation in the plane can be formed by composing a pair of reflections. First reflect a point P to its image P′ on the other side of line L 1. Then reflect P′ to its image P′′ on the other side of line L 2. If lines L 1 and L 2 make an angle θ with one another, then points P and P′′ will make an angle 2θ around point O, the ...