Questions and Answers
What is a Rigid Motion?
What is Translation in terms of rigid motion?
Moves a figure a fixed distance in a given direction.
What does Rotation refer to in rigid motion?
A transformation that 'turns' a figure about a fixed point called the center of rotation.
What is a Reflection in rigid motion?
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What is the line of reflection?
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What is the center of rotation?
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What is meant by Angle of Rotation?
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What does distance refer to in geometric terms?
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What does it mean to preserve in geometry?
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What is a Pre-Image?
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What is an image in geometry?
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Study Notes
Rigid Motions
- Rigid motion, also known as isometry, is a transformation that alters the position of a figure without altering its size or shape, resulting in congruent figures.
- Other terminology includes rigid transformation and congruence transformations.
Translation
- A translation moves a figure a fixed distance in a specified direction.
- In translations, all points of the figure move the same distance and in the same direction simultaneously.
Rotation
- Rotation is a type of rigid motion that involves turning a figure about a fixed point called the center of rotation.
- The movement occurs in a circular pattern around this center.
Reflection
- Reflection is a transformation that produces a mirror image of a figure over a specified line, known as the line of reflection.
- Each point in the figure remains equidistant from the line of reflection but is located on the opposite side.
Line of Reflection
- The line of reflection serves as the axis over which a figure is flipped to create its mirror image.
Center of Rotation
- The center of rotation is a specific fixed point around which shapes rotate to achieve a new position.
Angle of Rotation
- The angle of rotation refers to the number of degrees through which a figure is rotated during the transformation.
Distance
- Distance refers to length, which is a measure of the space between two points.
Preserve
- To preserve means to maintain the same properties, characteristics, or values throughout a transformation.
Pre-Image
- The pre-image is the original figure before any rigid motion has been applied and typically labeled (e.g., ABC).
Image
- The image is the new figure that results from the transformation of the original geometric figure, often labeled with primes to indicate the change (e.g., A'B'C').
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Description
Explore key concepts of rigid motions and isometries through these flashcards. Learn definitions and characteristics of transformations like translations while solidifying your understanding. Ideal for students studying geometry.
