# Rotation

Rotation is a type of rigid body transformation which changes the orientation of the object. The most common type of rotation is a rotation around the origin. To look at how rotations are performed, let’s take Point A, which is located at the coordinates of (a, b), as shown below: Using the next image, the length of the yellow line is the value of a, and the length of the green line is the value of b. To rotate the yellow and green lines, 90º around the origin gives us the following situation: To find the coordinates of where the image, point A’, we see that the green line is now in the negative x-direction, and the yellow line is now in the y-direction. So, the coordinates of A’ would be (-b, a). This is the way to perform any 90º counterclockwise around the origin, you switch the values of the and coordinate values and make the new x value negative. If we wanted to perform a 180º counterclockwise rotation on around the origin on point A, would be the same as doing a 90º counterclockwise rotation point A’. So, the coordinates of this new point would be (-a, -b). To perform a 270º counterclockwise rotation around the origin would move the point to coordinates (b, -a). Use the table below to help you determine the coordinates of a point after a rotation was performed:

Rotation Amount Direction Coordinates
Counterclockwise (a, b)
90º  Counterclockwise (-b, a)
180º  Counterclockwise (-a, -b)
270º  Counterclockwise (b, -a)
360º  Counterclockwise (a, b)
90º  Clockwise (b, -a)
180º  Clockwise (-a, -b)
270º  Clockwise (-b, a)
360º  Clockwise (a, b)