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. Examples include translations, rotations, and reflections.

Front

Define reflection in geometry.

Back

Reflection is a transformation that flips a figure over a line, creating a mirror image.

Front

What is the line of reflection?

Back

The line of reflection is the line over which a figure is reflected. Each point on the figure is equidistant from the line of reflection.

Front

Explain translation in geometry.

Back

Translation is a transformation that moves every point of a figure the same distance in the same direction.

Front

What is the rule for translating a point (x, y) to the right by 3 units and up by 2 units?

Back

The rule is (x, y) → (x + 3, y + 2).

Front

Define rotation in geometry.

Back

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

Front

What is symmetry?

Back

Symmetry is a property where a figure is invariant under certain transformations, such as reflection or rotation.

Front

What is the difference between line symmetry and rotational symmetry?

Back

Line symmetry occurs when a figure can be divided into two identical halves by a line, while rotational symmetry occurs when a figure can be rotated around a point and still look the same.

Front

How do you reflect a point (a, b) over the y-axis?

Back

The reflection of the point (a, b) over the y-axis is (-a, b).

Front

What happens to the coordinates of a point when it is reflected over the x-axis?

Back

When a point (x, y) is reflected over the x-axis, its coordinates become (x, -y).