Rigid Transformation Sequences

Front

What is a rigid transformation?

Back

A rigid transformation is a transformation that preserves the shape and size of a figure, meaning the original figure and its image are congruent.

Front

What are the three types of rigid transformations?

Back

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

Front

Define translation in the context of rigid transformations.

Back

Translation is a rigid transformation that slides a figure in a straight line from one position to another without changing its shape or size.

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

Explain rotation in rigid transformations.

Back

Rotation is a rigid transformation that turns a figure around a fixed point, known as the center of rotation, by a certain angle.

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 of the figure is mapped to a point directly opposite it across the x-axis, changing the sign of the y-coordinate.

Front

How do you perform a translation of a point (x, y) by (a, b)?

Back

To translate a point (x, y) by (a, b), you add a to the x-coordinate and b to the y-coordinate, resulting in the new point (x + a, y + b).

Front

What is the effect of a 90-degree counter-clockwise rotation about the origin on a point (x, y)?

Back

A 90-degree counter-clockwise rotation about the origin transforms the point (x, y) to (-y, x).

Front

What is the result of reflecting a point (x, y) over the y-axis?

Back

Reflecting a point (x, y) over the y-axis results in the point (-x, y).

Front

What is the sequence of transformations to map a figure to its image?

Back

The sequence of transformations includes identifying the type of transformations (translation, reflection, rotation) and their order to achieve the desired mapping.