Geometry: Reflection and Rotation Rules

What is the result of reflecting a point over the x-axis?

What is the result of reflecting a point over the y-axis?

What does reflecting over the line y = x result in?

What is the result of reflecting a point over the line y = -x?

What is the result of reflecting a point through the origin?

What is the rule for a 90 degree counterclockwise rotation?

What happens during a 180 degree rotation?

What is the result of a 270 degree counterclockwise rotation?

What is the rule for a 90 degree clockwise rotation?

What is the result of a 360 degree rotation?

What is the rule for a larger than 360 degree rotation?

What is the rule for a 270 degree clockwise rotation?

What is translation in terms of coordinate transformations?

What does dilation refer to in transformations?

What is rigid motion?

What are the three transformations that are rigid?

Reflection Rules

Reflecting over the x-axis transforms a point (x, y) to (x, -y).
Reflecting over the y-axis changes a point (x, y) to (-x, y).
Reflecting over the line y = x swaps coordinates, resulting in (y, x).
Reflecting over the line y = -x transforms the point to (-y, -x).
Reflecting through the origin changes (x, y) to (-x, -y).

Rotation Rules

A 90-degree counterclockwise rotation transforms (x, y) to (-y, x).
A 180-degree rotation changes the coordinates by negating both, translating (x, y) to (-x, -y).
A 270-degree counterclockwise rotation results in (y, -x).
A 90-degree clockwise rotation has the same effect as a 270-degree counterclockwise rotation, yielding (y, -x).
A 360-degree rotation leaves the point unchanged.
For a rotation larger than 360 degrees, subtract 360 degrees from the angle to find the equivalent transformation.
A 270-degree clockwise rotation matches a 90-degree counterclockwise rotation, transforming (x, y) to (-y, x).

Translation and Dilation Rules

Translation involves adding or subtracting values, which results in sliding the object; it shifts a point (x, y) to (x+1, y-2).
Dilation relates to multiplication or division, which alters the size of the object, changing (x, y) to (2x, 3y).

Rigid Motion

Rigid motion preserves both the size and shape of the figure.
The three transformations classified as rigid motions include reflection, translation, and rotation.

Test your knowledge of reflection and rotation rules in geometry with these flashcards. Each card presents a transformation rule with its corresponding coordinate changes. Perfect for students looking to reinforce their understanding of geometric transformations!