Rigid Transformations and Symmetry

Front

What is a rigid transformation?

Back

A transformation that preserves the shape and size of a figure, including translations, rotations, and reflections.

Front

Define reflection in geometry.

Back

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

Front

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

Back

The new coordinates will be (y, -x).

Front

What is the effect of a 180° rotation about the origin on the point (x, y)?

Back

The new coordinates will be (-x, -y).

Front

How do you reflect a point over the y-axis?

Back

Change the sign of the x-coordinate: (x, y) becomes (-x, y).

Front

What is the sequence of transformations?

Back

The order in which transformations are applied, which can affect the final position of the figure.

Front

If you reflect a point over the line y=x, what happens to its coordinates?

Back

The x and y coordinates are swapped: (x, y) becomes (y, x).

Front

What is the result of translating a point (x, y) by (a, b)?

Back

The new coordinates will be (x + a, y + b).

Front

Describe the transformation of rotating a figure 90° counterclockwise about the origin.

Back

The new coordinates will be (-y, x).

Front

What is symmetry in geometry?

Back

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