Unit A: Geometry

Chapter 2: Transformations


Creating a Rotation


Rotations are produced by turning an image. The four most common rotations are

  • quarter-turn (90°)
  • half turn (180°) 
  • three-quarter turn (270°)
  • full turn (360°)

The peace tower on the parliament building has four clocks. The hands on a clock rotate clockwise. Rotations in math can be made clockwise or counterclockwise.


Print off the graph with the rectangular smiley face. Then, view the following video demonstrating how rotations are perfomed.

Note:  When performing rotations, always refer to the top position of page when moving left (counterclockwise) or right (clockwise).

Rotations Video

After the paper with the smiley face is rotated 90° counterclockwise (to the left), the image will be in the top right-hand corner. The image is now on its side.


After a half turn to the left (180° counterclockwise), the image will be in the top left-hand corner. The image is now upside down.


After a three-quarter turn to the left (270° counterclockwise), the image will be in the bottom right-hand corner.


After a full rotation counterclockwise (to the left), the image will be in the same position as the original shape.