Questions and Answers
What is the definition of a reflection in a line?
What happens during a reflection in the x-axis?
Multiply its y-coordinate by -1.
To reflect a point in the line y=x, interchange the _____ and y-coordinates.
x
How do you translate a point in the coordinate plane along vector ⟨a, b⟩?
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What is the definition of a rotation?
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What is the center of rotation?
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What is the angle of rotation?
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To rotate a point 90° counterclockwise about the origin, multiply the y-coordinate by -1 and then interchange the ____ and y-coordinates.
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To rotate a point 180° counterclockwise about the origin, multiply the _____ and y-coordinates by -1.
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To rotate a point 270° counterclockwise about the origin, multiply the x-coordinate by -1 and then interchange the ____ and y-coordinates.
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What is a glide reflection?
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What is the composition of isometries?
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Reflections in parallel lines can be described by a translation vector that is perpendicular to the two lines, and ____ the distance between the two lines.
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Reflections in intersecting lines can be described by a rotation about the point where the lines intersect and through an angle that is _____ the measure of the acute or right angle formed by the lines.
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If a figure can be mapped onto itself by a reflection in a line, the figure has _________.
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What is the line of symmetry?
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If a figure can be mapped onto itself by a rotation between 0° and 360° about the center of the figure, the figure has _________.
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What is the center of symmetry?
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If a figure can be mapped onto itself by a reflection in a plane, the figure has ____________.
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If a figure can be mapped onto itself by a rotation between 0° and 360° in a line, the figure has _____________.
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Study Notes
Geometric Transformations
- Reflections in Intersecting Lines: Composite transformation linked to rotation about the intersection point and twice the acute or right angle formed by the lines.
- Reflection in a Line: Maps points to their image where the line acts as a perpendicular bisector for points not on the line, ensuring the point on the line remains unchanged.
- Reflection in the x-axis: Achieved by multiplying the y-coordinate of a point by -1.
- Reflection in Line y=x: Accomplished by interchanging the x- and y-coordinates of a point.
- Reflection in the y-axis: Involves multiplying the x-coordinate of a point by -1.
Translations and Rotations
- Translation: Maps each point along a given vector, effectively shifting the position of the figure without altering its orientation.
- Translation in the Coordinate Plane: For a vector ⟨a, b⟩, a point is translated by adding 'a' to the x-coordinate and 'b' to the y-coordinate.
- Rotation: Centers around a fixed point; if the point coincides with the center, it remains unchanged. Other points maintain a constant distance and specified angle from the center.
- Angle of Rotation: The degree measurement of the rotation about a fixed point.
- 90° Rotation in Coordinate Plane: Counterclockwise rotation achieved by multiplying the y-coordinate by -1 and then swapping x and y coordinates.
- 180° Rotation in Coordinate Plane: Involves multiplying both x and y coordinates by -1.
- 270° Rotation in Coordinate Plane: Accomplished by multiplying the x-coordinate by -1 first, then swapping x and y coordinates.
Symmetry
- Glide Reflection: A combination of translation followed by reflection in a line parallel to the translation vector.
- Composition of Isometries: Combines two or more isometric transformations that preserve distances and angles.
- Line Symmetry: Indicates a figure can match itself via a reflection across a specific line.
- Line of Symmetry: Divides a figure into two mirrored halves; can be vertical, horizontal, or diagonal.
- Rotational Symmetry: Describes a scenario where a figure maps to itself through rotation anywhere from 0° to 360° about its center.
- Center of Rotational Symmetry: The point around which a figure rotates symmetrically.
- Plane Symmetry: Achieved if a figure can reflect itself across a plane.
- Axis Symmetry: Indicates a figure's ability to map to itself through a rotation along a line.
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Description
Explore the key concepts and theorems in Chapter 9 of McGraw Hill Geometry. This quiz includes definitions for important terms like reflections in intersecting lines and translations. Perfect for students looking to reinforce their understanding of geometry concepts through flashcards.
