Rigid Transformations
Rigid Transformations (Translations, Reflections, & Rotations)
Table of Contents
- Reflections, Translations, & Rotations
- 1. Introduction (Read Only)
- 2. Translations
- 3. Translation Notes
- 4. Reflections
- 5. Reflection Notes
- 6. Rotations
- 7. Rotation Notes
1. Introduction (Read Only)
Rigid Transformation
A rigid transformation is a translation, rotation, or reflection. We sometimes also use the term to refer to a sequence of these.[br][img]https://cms-im.s3.amazonaws.com/3jKPNazeW2oVD62LpByH5K1y?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-10634.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-10634.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJFC4WL6K24MWHIRQ%2F20211006%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20211006T005957Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=aaea3cd333da83a553b06bf91a5b4bc2df0ecc561ecb010331e88bc196a8e3ff[/img]
Congruent
One figure is called congruent to another figure if there is a sequence of translations, rotations, and reflections that takes the first figure onto the second.[br][img]https://cms-im.s3.amazonaws.com/3jKPNazeW2oVD62LpByH5K1y?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-10634.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-10634.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJFC4WL6K24MWHIRQ%2F20211005%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20211005T222038Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a683a69626bd46173e7d7a856e1615e031a64c89fdb51b5f51a18257d09e6ca7[/img][br][b]Remember congruent means an object is the same (i.e. same shape, same size).[/b]
Image
If a transformation takes [math]A[/math] to [math]A'[/math], then [math]A[/math] is the original [b](pre-image) [/b]and [math]A'[/math] is the image.[br][img]https://cms-im.s3.amazonaws.com/RgKaJXTBPPa5Za24TFSDgWBM?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-10241.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-10241.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJFC4WL6K24MWHIRQ%2F20211005%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20211005T222038Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8d34dbd5909f05f17b3eadb7b68b98f4a4566057e4f31887df8a98fc53ce18ea[/img]