2D Rotation

Mentally rotating a shape by a specified angle in the plane.

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Mentally rotating a shape by a specified angle in the plane.

2D rotation involves mentally turning a shape around its center by a specified number of degrees. Clockwise rotation moves the shape in the same direction as clock hands; counterclockwise is the opposite. Common rotation angles are 90° (quarter turn), 180° (half turn), and 270° (three-quarter turn). The key skill is tracking how specific features of the shape move during rotation.

new_position = rotate(original_position, angle, center)

90° clockwise: top moves to right, right moves to bottom
180°: shape is upside-down, left-right reversed
270° clockwise = 90° counterclockwise

How to recognize it

Pick a distinctive feature (corner, point, asymmetric part)
Track where that feature moves during rotation
90° moves each side one position clockwise
Verify multiple features match the expected rotation

Common mistakes

Confusing clockwise with counterclockwise
Losing track of the original orientation
Not considering that 270° CW = 90° CCW

Step-by-step walkthrough

An arrow points upward. After rotating 90 degrees clockwise, which direction does it point?

Identify the starting orientation: the arrow points upward (toward 12 o'clock).
Understand 90 degrees clockwise means a quarter turn in the same direction clock hands move.
Visualize the arrow rotating: the tip moves from top toward the right side.
After 90 degrees clockwise, upward becomes rightward.

Answer: The arrow points to the right

Practice guidance

Spatial Reasoning