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 geometry.

Back

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

Front

What is a reflection in geometry?

Back

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

Front

What is 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

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

Back

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

Front

What is a line of symmetry?

Back

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

Front

How many lines of symmetry does a square have?

Back

A square has 4 lines of symmetry.

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

Describe the effect of a 90-degree clockwise rotation about the origin on the point (x, y).

Back

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