Rotation of Geometric Shapes

What is Rotation?

Rotation is a transformation that turns a shape around a fixed point, called the center of rotation, through a specific angle and direction.

Center of Rotation: The fixed point (often the origin).
Angle of Rotation: How far to rotate (e.g., 90^o, 180^o).
Direction: Clockwise (CW) or Counterclockwise (CCW).

Common Rotation Rules (around the origin)

Let (x,y) be the coordinate of a point. The following table gives the coordinates (x',y') of the point after rotations of angles of : 90, 180, 270 and 360 degrees.
The coordinates (x',y') are given in terms of (x,y) in the table below and can be checked in the interactive activity 1 below.

Rotation	Coordinate Rule
90^o CCW	(x, y) → (x' = -y, y' = x)
180^o	(x, y) → (x' = -x, y' = -y)
270^o CCW	(x, y) → (x ' = y, y' = -x)
360^o CCW	(x, y) → (x' = x, y' = y)

Interactive Activity 1: Rotate Your Own Points

Click to add points. Use the slider or angle input to rotate them. Points will be labeled A, B, C (in red) ... and their corresponding after rotation A', B', C' (in blue)...

Rotation Angle: degrees

Interactive Activity 2: Rotate a Triangle

Rotation Angle: degrees