rigid transformations and symmetry

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 remains congruent after the transformation.

Front

What are the types of rigid transformations?

Back

The types of rigid transformations include translations, rotations, and reflections.

Front

Define translation in the context of rigid transformations.

Back

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

Front

What is the rule for translating a point (x, y) by (a, b)?

Back

The rule for translating a point (x, y) by (a, b) is (x + a, y + b).

Front

What does it mean for figures to be congruent?

Back

Figures are congruent if they have the same shape and size, meaning one can be transformed into the other through rigid transformations.

Front

What is a reflection in geometry?

Back

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

Front

How do you reflect a point (x, y) over the line y = x?

Back

To reflect a point (x, y) over the line y = x, swap the coordinates to get (y, x).

Front

What is a rotation in geometry?

Back

A rotation is a type of rigid transformation that turns a figure around a fixed point, called the center of rotation, by a certain angle.

Front

What is the effect of a 90-degree rotation counterclockwise on a point (x, y)?

Back

The effect of a 90-degree rotation counterclockwise on a point (x, y) is to transform it to (-y, x).

Front

What is the line of symmetry?

Back

A line of symmetry is a line that divides a figure into two mirror-image halves.