Geometry: Rotations

Front

What is a rotation in geometry?

Back

A rotation in geometry is a transformation that turns a figure around a fixed point, known as the center of rotation, by a certain 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 in a geometric transformation.

Front

How do you determine the angle of rotation?

Back

The angle of rotation is the measure of the degree through which a figure is rotated around the center of rotation, typically measured in degrees or radians.

Front

What is the difference between clockwise and counterclockwise rotation?

Back

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

Front

How do you perform a 90-degree rotation clockwise on a point (x, y)?

Back

To perform a 90-degree clockwise rotation on a point (x, y), the new coordinates will be (y, -x).

Front

How do you perform a 180-degree rotation on a point (x, y)?

Back

To perform a 180-degree rotation on a point (x, y), the new coordinates will be (-x, -y).

Front

How do you perform a 270-degree rotation counterclockwise on a point (x, y)?

Back

To perform a 270-degree counterclockwise rotation on a point (x, y), the new coordinates will be (-y, x).

Front

What is the effect of rotation on the size and shape of a figure?

Back

Rotation does not change the size or shape of a figure; it only changes its position.

Front

What is a rotation matrix?

Back

A rotation matrix is a matrix that is used to perform a rotation in Euclidean space. For a 2D rotation by an angle θ, the rotation matrix is: [[cos(θ), -sin(θ)], [sin(θ), cos(θ)]].

Front

How do you find the image of a point after rotation?

Back

To find the image of a point after rotation, apply the appropriate rotation transformation based on the angle and direction of rotation to the original coordinates.