Rotating Shapes

Definition of Rotation in Maths

A rotation is a transformation that turns a shape around a fixed point without changing its size or shape.

Key Concepts in Rotation

• Centre of Rotation:
  The fixed point the shape turns around.

• Direction of Rotation:
  Either clockwise or anticlockwise.

• Angle of Rotation:
  How far the shape is turned, measured in degrees (e.g., 90°, 180°, 270°).

Key Idea

A rotation changes only the position of a shape. It keeps the shape the same size, same angles, only turned around the centre.

Task:

Rotate shape P by 90° clockwise about point O.

Steps to Rotate Using Tracing Paper

1. Trace the shape
   Place tracing paper over the shape and mark the key points on it carefully.

2. Mark the centre of rotation
   Put a clear dot on the tracing paper exactly at point O.

3. Rotate the tracing paper
   Turn the tracing paper 90° clockwise, keeping the pin or finger fixed on O.

4. Redraw the shape
   Plot the new position of each point, then join them to form the rotated shape.

Key Idea

Tracing paper lets you physically rotate the shape, so you can see exactly where every point moves.

Task:

Rotate shape P by 90° anticlockwise about point O.

Steps to Rotate Using Auxiliary Lines

1. Join each vertex to the centre
   Draw a straight line from every point on the shape to the centre of rotation O.

2. Rotate each line by the given angle
   Turn each line 90° anticlockwise.
   Keep the length of the line the same.

3. Mark the new points
   After rotating each line, place the new point at the same distance from O as the original point.

4. Draw the rotated shape
   Join the new points in the same order to form the rotated shape.

Key Idea

By rotating each point around the centre and keeping the distance the same, you create an accurate rotated shape.

To describe the rotation from shape P to shape Q, follow these steps:

1. Find the centre of rotation

• Join a point on P to its matching point on Q.
  Draw the perpendicular bisector of this line.
• Repeat with a second pair of matching points.
• The bisectors meet at (2, 3), this is the centre of rotation.
  
  

2. Work out the angle

• Draw a line from the centre of rotation (2, 3) to a point on shape P,
  and a line from the centre to the matching point on Q.
• Measure the angle between these two lines. In this case, the angle between the two lines is a right angle, so the rotation is 90°.
  
  

3. Work out the direction

• Moving from right → up is moving anticlockwise around the centre.
• So the rotation is anticlockwise.

Final Description

Shape P is rotated 90° anticlockwise about the point (2, 3) to get shape Q.