16.1 Translations
Links and useful resources
- gr10's Geometry >>>START HERE<<<
- AoPS Online Textbook
- AoPS Alcumus
- Big Ideas Geometry textbook
- GeoGebra Online Geometry Constuction Tool
- Two-column math templates
- Proofs unit slides from mathgiraffe.com
- Proofs unit printables for two-column proofs
Concept summary and connections
- Terminology: Translation of
is - Translation: Moving something. Specify a direction and a distance (remind you of anything that starts with a 'v' and sounds like Hector?)
- Mapping: an operation that turns one thing into another one. Example: You could map point (2,2) into (3,4) by adding (1,2) to it.
Lesson and worked examples
- Anything can be translated (points, figures, etc.)
- A translated figure is congruent to the original
- With vectors, a translation is done by adding the same vector to all points of the figure.
Anything you can prove about the internal properties of a diagram (i.e. only relating the diagram parts to its own other parts) remains true about all of its translations and rotations. Sometimes it's useful to apply some transformations before you start a proof, mostly just to make things easier for you to see as a human.
Understanding transformations is often more about learning what stays the same rather than what changes. In the three basic transformations we’ll study in this chapter, everything will stay the same for each transformed figure except its location and orientation.
Media resources
- Youtube search for "Terminology: Translation of
is " - Youtube search for "Translation: Moving something. Specify a direction and a distance (remind you of anything that starts with a 'v' and sounds like Hector?)"
- Youtube search for "Mapping: an operation that turns one thing into another one. Example: You could map point (2,2) into (3,4) by adding (1,2) to it. "
Guided practice
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A fixed point of a transformation is a point that is its own image. The identity transformation is the transformation that maps every point to itself. In other words, the identity is the ‘do nothing’ transformation. Can a translation that is not the identity have a fixed point?
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