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 determined by the amount of turn from the original position of the figure to its new position, measured in degrees or radians.

Front

What is the difference between clockwise and counterclockwise rotation?

Back

Clockwise rotation is a turn to the right, while counterclockwise rotation is a turn to the left, as viewed from above the center of rotation.

Front

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

Back

To rotate a point (x, y) 90 degrees clockwise, the new coordinates will be (y, -x).

Front

How do you perform a rotation of 90 degrees counterclockwise on a point (x, y)?

Back

To rotate a point (x, y) 90 degrees counterclockwise, the new coordinates will be (-y, x).

Front

What is the effect of rotating a figure 180 degrees?

Back

Rotating a figure 180 degrees results in the figure being turned upside down, with each point moving to a position directly opposite its original location.

Front

What is the formula for rotating a point (x, y) by an angle θ around the origin?

Back

The new coordinates (x', y') after rotating a point (x, y) by an angle θ around the origin are given by: x' = x*cos(θ) - y*sin(θ), y' = x*sin(θ) + y*cos(θ).

Front

What is a rotation matrix?

Back

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

Front

How does rotation affect the size and shape of a figure?

Back

Rotation does not affect the size or shape of a figure; it only changes the position of the figure in the plane.