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  2. Rotations and reflections in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotations_and_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 2 θ around point O , the intersection of L 1 and L 2 .

  3. Euclidean plane isometry - Wikipedia

    en.wikipedia.org/wiki/Euclidean_plane_isometry

    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.

  4. Rotation (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Rotation_(mathematics)

    The rotation is acting to rotate an object counterclockwise through an angle θ about the origin; see below for details. Composition of rotations sums their angles modulo 1 turn, which implies that all two-dimensional rotations about the same point commute. Rotations about different points, in general, do not commute.

  5. Rotation of axes in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotation_of_axes_in_two...

    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 y axes counterclockwise through an angle .

  6. Reflection (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Reflection_(mathematics)

    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.

  7. Euclidean group - Wikipedia

    en.wikipedia.org/wiki/Euclidean_group

    Glide reflections with translation by the same distance are in the same class. In 3D: Inversions with respect to all points are in the same class. Rotations by the same angle are in the same class. Rotations about an axis combined with translation along that axis are in the same class if the angle is the same and the translation distance is the ...

  8. Download, install, or uninstall AOL Desktop Gold - AOL Help

    help.aol.com/articles/aol-desktop-downloading...

    Learn how to download and install or uninstall the Desktop Gold software and if your computer meets the system requirements.

  9. Congruence (geometry) - Wikipedia

    en.wikipedia.org/wiki/Congruence_(geometry)

    Translate the first figure by this vector so that these two vertices match. Third, rotate the translated figure about the matched vertex until one pair of corresponding sides matches. Fourth, reflect the rotated figure about this matched side until the figures match. If at any time the step cannot be completed, the polygons are not congruent.

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