which rigid transformation could be defined as a turnaround, a centerpoint determined by an angle measured in degrees
The rigid transformation that can be defined as a turnaround, with a centerpoint determined by an angle measured in degrees, is a rotation.
The rigid transformation that can be defined as a turnaround or rotation is called a rotation transformation. The center point, which determines the rotation, is defined by an angle measured in degrees.
The rigid transformation that fits this description is a rotation. A rotation is a transformation that turns or rotates an object around a fixed point called the center of rotation. The center of rotation is determined by the given angle measured in degrees.
To perform a rotation, follow these steps:
1. Identify the center of rotation: This is the given point around which the object will rotate.
2. Determine the angle of rotation: The angle, measured in degrees, specifies how much the object will be turned.
3. Choose the direction of rotation: Determine whether the rotation will be clockwise or counterclockwise.
4. Apply the rotation: Rotate each point of the object by the specified angle around the center of rotation.
To find the coordinates of each point after the rotation, you can use the following formulas:
For a counterclockwise rotation:
NewX = OldX * cos(theta) - OldY * sin(theta)
NewY = OldX * sin(theta) + OldY * cos(theta)
For a clockwise rotation:
NewX = OldX * cos(theta) + OldY * sin(theta)
NewY = -OldX * sin(theta) + OldY * cos(theta)
In these formulas, (OldX, OldY) represent the original coordinates of a point, (NewX, NewY) are the new coordinates after the rotation, and theta is the angle of rotation in radians.
By using these formulas, you can perform a rotation as a rigid transformation around a centerpoint determined by an angle measured in degrees.