What is a Glide Reflection?
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1 Info Finite Shapes atterns Reflections Rotations Translations Glides Classifying What is a Glide Reflection? A glide reflection is a cobination of a translation and a reflection. The vector of translation v and the axis of reflection ust be parallel to each other.
2 Info Finite Shapes atterns Reflections Rotations Translations Glides Classifying Exaples Q R v
3 Info Finite Shapes atterns Reflections Rotations Translations Glides Classifying Exaples Q Q * Q* R R R* v v
4 Info Finite Shapes atterns Reflections Rotations Translations Glides Classifying Exaples Q Q * Q* R R R* v v Q * Q* R v R* R Q
5 Info Finite Shapes atterns Reflections Rotations Translations Glides Classifying Exaples Since the vector of translation and the axis of reflection are parallel, it does not atter which otion is done first in the glide reflection. Q * R R* v R Q* Q
6 Info Finite Shapes atterns Reflections Rotations Translations Glides Classifying roperties of Glide Reflections 1. A glide reflection is copletely deterined by two point-iage pairs. The axis of reflection is the line passing through the two idpoints of the segents and QQ. Use the axis of reflection to find an interediate point. For exaple, the iage of under the reflection is the interediate point. Finally, the vector of translation is the vector connecting to.
7 Info Finite Shapes atterns Reflections Rotations Translations Glides Classifying Two oint-iage airs Deterine a Glide Reflection Q Q
8 Info Finite Shapes atterns Reflections Rotations Translations Glides Classifying Two oint-iage airs Deterine a Glide Reflection Q Q Q Q
9 Info Finite Shapes atterns Reflections Rotations Translations Glides Classifying Two oint-iage airs Deterine a Glide Reflection Q Q Q Q Q v Q* Q
10 Info Finite Shapes atterns Reflections Rotations Translations Glides Classifying roperties of Glide Reflections Does a glide reflection have any fixed points?
11 Info Finite Shapes atterns Reflections Rotations Translations Glides Classifying roperties of Glide Reflections Does a glide reflection have any fixed points? No. 2. Since a translation has no fixed points, a glide reflection has no fixed points.
12 Info Finite Shapes atterns Reflections Rotations Translations Glides Classifying roperties of Glide Reflections Does a glide reflection have any fixed points? No. 2. Since a translation has no fixed points, a glide reflection has no fixed points. Is a glide reflection a proper or iproper otion?
13 Info Finite Shapes atterns Reflections Rotations Translations Glides Classifying roperties of Glide Reflections Does a glide reflection have any fixed points? No. 2. Since a translation has no fixed points, a glide reflection has no fixed points. Is a glide reflection a proper or iproper otion? Iproper. Why? 3. A glide reflection is an iproper otion.
14 Info Finite Shapes atterns Reflections Rotations Translations Glides Classifying roperties of Glide Reflections Given a glide reflection with translation vector v and axis of reflection, how can we undo the otion?
15 Info Finite Shapes atterns Reflections Rotations Translations Glides Classifying roperties of Glide Reflections Given a glide reflection with translation vector v and axis of reflection, how can we undo the otion? To undo the translation, we ust apply the translation with vector v. To undo the reflection, we ust apply the reflection with the sae axis of reflection.
16 Info Finite Shapes atterns Reflections Rotations Translations Glides Classifying roperties of Glide Reflections Given a glide reflection with translation vector v and axis of reflection, how can we undo the otion? To undo the translation, we ust apply the translation with vector v. To undo the reflection, we ust apply the reflection with the sae axis of reflection. 4. When a glide reflection with vector v and axis of reflection is followed by a glide reflection with vector v and axis of reflection, we obtain the identity otion.
17 Info Finite Shapes atterns Reflections Rotations Translations Glides Classifying Suary of Motions oint-iage Rigid Motion Specified by roper/iproper Fixed oints airs Needed Reflection Axis of reflection l Iproper All points on l One Rotation* Rotocenter O and angle α roper O only Two Translation Vector of translation v roper None One Glide Reflection Vector of translation v and Iproper None Two axis of reflection l *Identity roper All points (0 rotation)
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