Questions and Answers
What is the main characteristic of a rigid transformation?
In a reflection, the figure is distorted over the line of reflection.
False
What is the center of rotation in a rotation transformation?
The fixed point around which the figure turns.
A translation moves every point of a figure the same distance in the same ______.
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Match the types of rigid transformations to their definitions:
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Study Notes
Rigid Transformations
- Rigid transformations preserve the shape and size of figures, preventing distortion.
- Distances between points and angles remain unchanged during rigid transformations.
Types of Rigid Transformations
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Translation
- Moves every point of a figure the same distance in a specific direction.
- The shape and orientation of the figure remain constant; only the position changes.
- Example: Translating a triangle 3 units right and 2 units up shifts all points equally.
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Rotation
- Rotates a figure around a fixed point, known as the center of rotation, by a specified angle.
- Distances from the center of rotation to all points on the figure remain the same.
- Example: A square rotated 90° clockwise around its center maintains congruency to its original position.
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Reflection
- Flips a figure over a line, referred to as the line of reflection.
- Creates a mirror image of the figure, with each point having a corresponding point on the opposite side of the line.
- Example: Reflecting a pentagon over the y-axis results in each point moving to an equal distance on the opposite side of the axis.
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Description
Explore the concept of rigid transformations in geometry, focusing on how they preserve the shape and size of figures. This quiz covers the three main types of rigid transformations: translation, rotation, and reflection with definitions and examples.
