Composition of Rigid Transformations

Front

What is a rigid transformation?

Back

A rigid transformation is a transformation that preserves the shape and size of a figure, meaning the figure's dimensions remain unchanged.

Front

What are the three main types of rigid transformations?

Back

The three main types of rigid transformations are translations, rotations, and reflections.

Front

What is a translation in geometry?

Back

A translation is a rigid transformation that slides a figure from one position to another without turning it.

Front

How does a rotation transformation work?

Back

A rotation transformation turns a figure around a fixed point, called the center of rotation, by a specified angle.

Front

What is a reflection in geometry?

Back

A reflection is a rigid transformation that flips a figure over a line, creating a mirror image.

Front

What is the effect of a 90-degree rotation on a point in the coordinate plane?

Back

A 90-degree rotation counterclockwise around the origin transforms the point (x, y) to (-y, x).

Front

What does it mean to reflect a figure over the x-axis?

Back

Reflecting a figure over the x-axis means that each point (x, y) of the figure is transformed to (x, -y).

Front

What is the result of performing a translation followed by a rotation?

Back

The result is a new position and orientation of the figure, depending on the direction and distance of the translation and the angle of rotation.

Front

How can you describe the composition of transformations?

Back

The composition of transformations is the combination of two or more transformations applied in sequence to a figure.

Front

What is the difference between a translation and a reflection?

Back

A translation moves a figure without changing its orientation, while a reflection flips a figure over a line, changing its orientation.