Transformations: Rotation and Reflection Rules

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.

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.