What is the rule for a glide reflection?
A glide reflection is a composition of transformations.In a glide reflection, a translation is first performed on the figure, then it is reflected over a line. Therefore, the only required information is the translation rule and a line to reflect over. A common example of glide reflections is footsteps in the sand.
What is the order of a glide reflection?
A popular sequence of transformations in which a specific pattern of a reflection followed by translation occurs is called a glide reflection. There will be a reflection of a figure, followed by a translation (a “glide” or slide) of the figure along the line of reflection.
What is a glide reflection defined by?
A glide reflection is a combination of a reflection and a translation. Glide reflections consist of translating a figure by sliding it along a line, then reflecting the figure over an axis of reflection.
What is an example of a glide reflection?
A typical example of glide reflection in everyday life would be the track of footprints left in the sand by a person walking on a beach. For any symmetry group containing some glide reflection symmetry, the translation vector of any glide reflection is one half of an element of the translation group.
What is a slide reflection?
Translation is when we slide a figure in any direction. Reflection is when we flip a figure over a line. Rotation is when we rotate a figure a certain degree around a point. Dilation is when we enlarge or reduce a figure.
Is glide reflection isometry?
A glide-reflection is an isometry that is the product of a reflection and a translation in the direction of the axis of the reflection.
Why is a glide reflection called a glide reflection?
Description. The combination of a reflection in a line and a translation in a perpendicular direction is a reflection in a parallel line. Thus the effect of a reflection combined with any translation is a glide reflection, with as special case just a reflection. These are the two kinds of indirect isometries in 2D.
What do glide reflections preserve?
Glide reflection changes the orientation: if a polygon is traversed clockwise, its image is traversed counterclockwise, and vice versa. Reflection is isometry: a glide reflection preserves distances. Reflection preserves angles.
What is a glide reflection tessellation?
Firstly, a glide reflection tessellation is a pattern with no gaps or overlaps (e.g. a tessellation), made by flipping (e.g. reflecting) and sliding (e.g. translating) a shape to repeat it.
Which is the correct formula for glide reflection?
Glide Reflection Formula 1 Reflection in x-axis: (x, y) → (x, -y) 2 Reflection in y-axis: (x, y) → (-x, y) 3 Reflection in y = x: (x, y) → (y, x) 4 Reflection in y = -x: (x, y) → (-y, -x)
What are glide reflections and congruence in geometry?
Glide Reflections and Congruence. A glide reflection is the composition of a reflection, and a translation in a vector parallel to the line of reflection. This image gets the idea across: (The figure is from Richard Brown’s excellent but dated and out-of-print Transformational Geometry)
Why is the glide reflection a unique case?
I offer three arguments for the unique significance of the glide reflection: In a glide reflection, the two component transformations can be performed in either order. This turns out to be super-convenient, and is not the case with the other cases mentioned above.
Can you do glide reflection in high school?
Glide reflections belong in such an ideal-world side trip. In the less-than-ideal world we live in, they can provide some good exercises and problems in grades 8-10, serve as an enrichment topic in precalculus, or be part of a full-fledged unit in a Year 4 advanced geometry elective. But enough introduction.