Transformations: Rotations and Dilations

Rotations

The first transformation we are going to look at in this section is rotations.

A rotation simply “rotates” an object around a given point.  It does not change the size or shape, but it does change the orientation of the object.

Take a look at the following rotations.

Purple arrow pointing right, rotated counterclockwise 90 degrees to point up, rotated counterclockwise 90 degrees to point left.
Rotation of an Arrow

 

Notice that the dark purple arrow has been rotated 90° counterclockwise around the center point to make the lighter purple arrow pointing up.  It is then rotated another 90° counter clockwise to make the lightest purple arrow pointing left.  The result is an arrow that is the same size and shape, but has a different orientation.

 

Green triangle rotated clockwise 90 degrees, then rotated another 90 degrees
Rotation of a Triangle

 

Notice that the dark green triangle has been rotated 90° clockwise around the center point to make the lighter green triangle.  It is then rotated another 90° clockwise to make the lightest green triangle.  The result is a triangle that is the same size and shape, but a different orientation.

 

Smiley face rotating around a center point

Rotation Around a Point

 

Rotations can be clockwise or counterclockwise and can be any degree.  Notice in this case that the dark orange smiley face has been rotated counterclockwise around the center point a few times.  Each rotation is approximately 60°.  The result is the lightest smiley face that is the same size and shape, but a different orientation.