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The image of a figure by a reflection is its mirror image in the axis or plane of reflection. For example the mirror image of the small Latin letter p for a reflection with respect to a vertical axis (a vertical reflection) would look like q. Its image by reflection in a horizontal axis (a horizontal reflection) would look like b.
For an arbitrary shape, the axiality of the shape measures how close it is to being bilaterally symmetric. It equals 1 for shapes with reflection symmetry, and between two-thirds and 1 for any convex shape. In 3D, the cube in which the plane can configure in all of the three axes that can reflect the cube has 9 planes of reflective symmetry. [3]
An xy-Cartesian coordinate system rotated through an angle to an x′y′-Cartesian coordinate system In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and ...
Reflection. Reflections, or mirror isometries, denoted by F c,v, where c is a point in the plane and v is a unit vector in R 2.(F is for "flip".) have the effect of reflecting the point p in the line L that is perpendicular to v and that passes through c.
Likewise, (x, −y) are the coordinates of its reflection across the first coordinate axis (the x-axis). In more generality, reflection across a line through the origin making an angle θ {\displaystyle \theta } with the x-axis, is equivalent to replacing every point with coordinates ( x , y ) by the point with coordinates ( x ′, y ′) , where
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The dihedral group D 2 is generated by the rotation r of 180 degrees, and the reflection s across the x-axis. The elements of D 2 can then be represented as {e, r, s, rs}, where e is the identity or null transformation and rs is the reflection across the y-axis. The four elements of D 2 (x-axis is vertical here) D 2 is isomorphic to the Klein ...
A drawing of a butterfly with bilateral symmetry, with left and right sides as mirror images of each other.. In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object onto itself (i.e., the object has an invariance under the transform). [1]