Rotations Wjec-Eduqas Higher

Rotations

What is a rotation?

• A rotation turns a shape around a point

  • This is called the centre of rotation

• The rotated image is the same size as the original image

  • It will have a new position and orientation

• If the centre is a point on the original shape then that point is not changed by the rotation

  • It is called an invariant point

How do I rotate a shape?

• STEP 1

  Place the tracing paper over page and draw over the original object

• STEP 2

  Place the point of your pencil on the centre of rotation

• STEP 3

  Rotate the tracing paper by the given angle in the given direction

  • The angle will be 90°, 180° or 270°

• STEP 4
  Carefully draw the image onto the coordinate grid in the position shown by the tracing paper

How do I describe a rotation?

• To describe a rotation, you must:

  • State that the transformation is a rotation

  • State the centre of rotation

  • State the angle of rotation 

    • This will be 90°, 180° or 270°

  • State the direction of rotation

    • Clockwise or anti-clockwise

    • A direction is not required if the angle is 180°

    • 90° clockwise is the same as 270° anti-clockwise

• To find the centre of rotation:

  • If the rotation is 90° or 270°

    • Use tracing paper and start on the original shape

    • Try a point as the centre and rotate the original shape

    • If the rotated shape matches the image then that point is the centre

    • Otherwise keep picking points until one works

  • If the rotation is 180°

    • Draw lines connecting each vertex on the original shape with the corresponding vertices on the image

    • These lines will intersect at the centre of rotation

How do I reverse a rotation?

• If a shape has been rotated to a new position, you can perform a single transformation to return the shape to its original position

• A rotation can be reversed by simply reversing the direction of rotation

  • The angle of rotation is the same

  • The centre of rotation is the same

• For a shape rotated by 45º in a clockwise direction about the point (0, 3)

  • The reverse transformation is

    • a rotation of 45º

    • in an anti-clockwise direction

    • about the point (0, 3)