Geometric Transformations Rotations

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a figure around a fixed point, known as the center of rotation, by a specified angle in a specified direction.

Front

What is the center of rotation?

Back

The center of rotation is the fixed point around which a figure is rotated.

Front

How do you perform a 90° clockwise rotation about the origin?

Back

To perform a 90° clockwise rotation about the origin, the coordinates (x, y) of a point are transformed to (y, -x).

Front

What is the rule for a 180° rotation about the origin?

Back

The rule for a 180° rotation about the origin is (x, y) → (-x, -y).

Front

What happens to the coordinates of a point after a 270° counterclockwise rotation about the origin?

Back

After a 270° counterclockwise rotation, the coordinates (x, y) are transformed to (-y, x).

Front

What does it mean for a transformation to preserve congruence?

Back

A transformation preserves congruence if the original figure and the transformed figure are identical in shape and size.

Front

What is the difference between clockwise and counterclockwise rotation?

Back

Clockwise rotation moves in the direction of the hands of a clock, while counterclockwise rotation moves in the opposite direction.

Front

If point A(2, 3) is rotated 180° about the origin, what are the new coordinates?

Back

The new coordinates of point A after a 180° rotation are A'(-2, -3).

Front

What is the effect of a rotation on the orientation of a figure?

Back

A rotation can change the orientation of a figure, but it preserves the shape and size.

Front

How do you determine the new position of a triangle after rotation?

Back

To determine the new position of a triangle after rotation, apply the appropriate rotation rule to each vertex of the triangle.