![]() Every glide reflection has a mirror line and translation distance. ![]() Every reflection has a mirror line.Ī glide reflection is a mirror reflection followed by a translation parallel to the mirror. Every rotation has a rotocenter and an angle.Ī reflection fixes a mirror line in the plane and exchanges points from one side of the line with points on the other side of the mirror at the same distance from the mirror. Every translation has a direction and a distance.Ī rotation fixes one point (the rotocenter) and everything rotates by the same amount around that point. In a translation, everything is moved by the same amount and in the same direction. There are four types of rigid motions that we will consider: translation, rotation, reflection, and glide reflection. A glide reflection is a mirror reflection followed by a translation parallel to the mirror. Together, the four are known as the basic rigid motions of the plane, which, in view of the fact that there are no others, is really a stupid nomenclature.Any way of moving all the points in the plane such thatĪ) the relative distance between points stays the same andī) the relative position of the points stays the same. It can be shown that there are only four plane isometries: translation, reflection, rotation and glide reflection. Isometry, also called rigid motion, is a transformation (of the plane in our case) that preserves distances. The importance of the glide reflection lies in the fact that it is one of the four isometries of the plane. ![]() If the translation part is trivial, the glide reflection becomes a common reflection and inherits all its properties.Īll these properties are implied by the definition of the glide reflection being a product of reflection and translation. Unless the translation part of a glide reflection it trivial (defined by a 0 vector), the glide reflection has neither fixed points, nor fixed lines, save the axis of reflection itself. Reflection maps parallel lines onto parallel lines. ![]() Reflection is isometry: a glide reflection preserves distances. The axes of the glide reflections meet at a rotation center of order 2. The rotation centers lie on the reflection axes. Glide reflection changes the orientation: if a polygon is traversed clockwise, its image is traversed counterclockwise, and vice versa. p4m symmetry has rotations of orders 2 and 4 reflections in the vertical, horizontal, and diagonal axes and glide reflections. The following observations are noteworthy: If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet. Identify each mapping as a reflection, translation, rotation, or glide reflection. This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Name the isometry that maps one onto the other. One can easily verify that the same result is obtained by first reflecting and then translating the image. The order of the two constituent transforms (translation and reflection) is not important. Because a glide reflection is a composition of a translation and a. Glide reflection is a composite transformation which is a translation followed by a reflection in line parallel to the direction of translation. What relationship do you see between x to x and y to y C.
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