Transformations: Rotation and Reflection Rules

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the result of a 90 degree rotation counterclockwise around the origin?

(-y, x) (correct)

(x, -y)

(-x, -y)

(y, -x)

What is the result of a 90 degree rotation clockwise about the origin?

(y, -x) (correct)

(-x, -y)

(-y, x)

(x, -y)

Which transformation represents a 180 degree rotation?

(-y, -x)

(y, x)

(x, -y)

(-x, -y) (correct)

What is the result of a 270 degree rotation clockwise about the origin?

(-y, x) Signup and view all the answers

What is the result of a 270 degree rotation counterclockwise about the origin?

(y, -x) Signup and view all the answers

What is the reflection over the x-axis transformation?

(x, y) --> (x, -y) Signup and view all the answers

What is the reflection over the y-axis transformation?

(x, y) --> (-x, y) Signup and view all the answers

What is the reflection over the line y = x transformation?

(x, y) --> (y, x) Signup and view all the answers

What is the translation rule?

(x, y) --> (x + a, y + b) Signup and view all the answers

What is a transformation?

A change in location, size or orientation of a figure Signup and view all the answers

What is a pre-image?

The original figure Signup and view all the answers

What is an image in geometry?

The figure after the transformation Signup and view all the answers

What does reflection mean?

Flips a figure over a line of symmetry Signup and view all the answers

What does translation mean?

Slides a figure to a different location Signup and view all the answers

What does rotation mean?

Turns a figure around a fixed point Signup and view all the answers

What does (x, y) --> (x + 1, y - 6) mean?

One right and six down Signup and view all the answers

What does (x, y) --> (-y, x) represent?

90 degrees counterclockwise rotation Signup and view all the answers

What does (x, y) --> (y, -x) represent?

90 degrees clockwise rotation Signup and view all the answers

What does (x, y) --> (-x, -y) represent?

180 degrees rotation Signup and view all the answers

Study Notes

Rotation Transformations

90 Degree Counterclockwise Rotation: Transforms a point (x, y) to (-y, x).
90 Degree Clockwise Rotation: Transforms a point (x, y) to (y, -x).
180 Degree Rotation: Both clockwise and counterclockwise transformations change a point (x, y) to (-x, -y).
270 Degree Clockwise Rotation: A point (x, y) becomes (-y, x).
270 Degree Counterclockwise Rotation: A point (x, y) changes to (y, -x).

Reflection Transformations

Reflection Over the X-Axis: The transformation (x, y) results in (x, -y), flipping the point over the x-axis.
Reflection Over the Y-Axis: The transformation (x, y) results in (-x, y), flipping the point over the y-axis.
Reflection Over the Line y = x: A point (x, y) maps to (y, x), switching the coordinates.
Reflection Over the Line y = -x: A point (x, y) transforms to (-y, -x), flipping across y = -x.

General Concepts

Transformation: Refers to any change in location, size, or orientation of a figure.
Pre-Image: The original figure before any transformations are applied.
Image: The resulting figure after a transformation.
Reflection: A flip over a specific line of symmetry.
Translation: Slides a figure from one position to another without altering its shape or size.
Rotation: Involves turning a figure around a fixed point.

Specific Rules

Translation Rule: Moves a point (x, y) to (x + a, y + b), adjusting its position by 'a' units horizontally and 'b' units vertically.
Example of (x, y) → (x + 1, y - 6): Indicates movement one unit right and six units down.

Examples

Reflection Examples: Specific transformations showing how points change, such as reflecting a triangle over the x-axis.
Translation Examples: Demonstrating how figures shift on a coordinate grid.
Rotation Examples: Illustrating the effect of rotating shapes through angles like 90 or 180 degrees.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Explore the fundamental rules of geometric transformations, focusing on rotations and reflections. This quiz includes key definitions and coordinate changes for various degrees of rotation, both clockwise and counterclockwise. Perfect for students mastering coordinate geometry concepts.