Final answer:
A transformation in mathematics refers to a change in the position, shape, or orientation of a geometric figure. The different types of transformations include translation, reflection, rotation, and dilation. An isometry, also known as a rigid motion, is a type of transformation that preserves both shape and size. The transformations that are isometries are translation, reflection, and rotation, while dilation is not an isometry.
Step-by-step explanation:
A. What is a transformation?
A transformation in mathematics refers to a change in the position, shape, or orientation of a geometric figure. It involves moving each point of a figure to a new position while preserving certain properties.
B. What are the different types of transformations?
The different types of transformations include:
- Translation: Moving a figure in a straight line without changing its shape.
- Reflection: Creating a mirror image of a figure over a line called the line of reflection.
- Rotation: Turning a figure around a fixed point called the center of rotation.
- Dilation: Enlarging or reducing a figure by a scale factor, while keeping its shape.
C. What is an isometry (rigid motion)?
An isometry, also known as a rigid motion, is a type of transformation that preserves both shape and size. It means that the original figure and its image after the transformation are congruent.
D. Which transformations are isometries? Which transformations are not isometries?
The transformations that are isometries (rigid motions) are:
- Translation
- Reflection
- Rotation
The transformation that is not an isometry is:
- Dilation