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⟩?
Signup and view all the answers
What is the definition of a rotation?
Signup and view all the answers
What is the center of rotation?
Signup and view all the answers
What is the angle of rotation?
Signup and view all the answers
To rotate a point 90° counterclockwise about the origin, multiply the y-coordinate by -1 and then interchange the ____ and y-coordinates.
Signup and view all the answers
To rotate a point 180° counterclockwise about the origin, multiply the _____ and y-coordinates by -1.
Signup and view all the answers
To rotate a point 270° counterclockwise about the origin, multiply the x-coordinate by -1 and then interchange the ____ and y-coordinates.
Signup and view all the answers
What is a glide reflection?
Signup and view all the answers
What is the composition of isometries?
Signup and view all the answers
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.
Signup and view all the answers
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.
Signup and view all the answers
If a figure can be mapped onto itself by a reflection in a line, the figure has _________.
Signup and view all the answers
What is the line of symmetry?
Signup and view all the answers
If a figure can be mapped onto itself by a rotation between 0° and 360° about the center of the figure, the figure has _________.
Signup and view all the answers
What is the center of symmetry?
Signup and view all the answers
If a figure can be mapped onto itself by a reflection in a plane, the figure has ____________.
Signup and view all the answers
If a figure can be mapped onto itself by a rotation between 0° and 360° in a line, the figure has _____________.
Signup and view all the answers
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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.