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 translation in geometry.

Back

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

Front

What is reflection in geometry?

Back

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

Front

Explain 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 line symmetry?

Back

Line symmetry (or reflectional symmetry) occurs when a figure can be divided into two identical halves that are mirror images of each other.

Front

What is rotational symmetry?

Back

Rotational symmetry is when a figure can be rotated around a center point and still look the same at certain angles.

Front

How do you determine the distance between points after reflection across parallel lines?

Back

The distance between the original point and its image after reflection across two parallel lines is twice the distance between the two lines.

Front

What is the effect of a 180-degree rotation about the origin?

Back

A 180-degree rotation about the origin transforms a point (x, y) to (-x, -y).

Front

What does it mean to translate a figure right 3 and down 2?

Back

To translate a figure right 3 and down 2 means to move every point of the figure 3 units to the right and 2 units down.