Final answer:
A rigid motion is a transformation that moves an object without altering its shape or size. Translations, rotations, and reflections are all types of rigid motions, preserving the distances between points on the object.
Step-by-step explanation:
Rigid motion refers to a transformation in which an object is moved to a different location without altering its shape or size. There are several types of transformations that are considered rigid motions: translations, rotations, and reflections. These transformations maintain the distance between points, meaning the object's shape and size remain unchanged. Here's how we can understand each one:
- Translations involve sliding the entire object a certain distance in a given direction. It's like pushing a book across a table; the book moves but doesn't change shape or orientation.
- Rotations turn the object around a fixed point or axis. Like spinning a coin on a table, the coin's position changes but its shape does not.
- Reflections flip the object over a line, creating a mirror image. It's akin to seeing your reflection in a pond; you appear upside down, but your shape is preserved.
We can conclude that these are rigid motions due to the property that distances between points on the object are conserved during the transformation.