0580

Transformations

Vectors and Transformations

Doing one

  • A rotation turns the shape about a fixed point, the centre of rotation, through a multiple of 90°
  • Tracing paper is provided in the examination and is by far the most reliable method
    • Trace the object, press a pencil point onto the centre, turn the paper through the given angle, then copy the image across
    • Drawing an arrow on the tracing paper first shows at a glance how far it has turned
Before rotating: the centre of rotation is marked with a red cross, an arrow shows the direction of the turn, and one vertex of the shape is marked so its journey can be followed
Source: Rotations by Save My Exams
  • The size and shape are unchanged, only the position and the orientation
  • If the centre lies on the shape, that point is invariant
Shape A rotated clockwise about a centre of rotation marked at (−4, 0), each vertex swinging round on the arc shown to give the image B on the other side of the y-axis
Source: Rotations by Save My Exams
Exam tip

All three parts are needed: the angle, the direction and the centre. Sixteen of the 43 mark schemes turn on the direction word alone, and a quarter turn described only as "90°" is incomplete. Tracing paper is on the equipment list for exactly this.

Describing one

  • Say rotation, then give the angle with its direction, then the centre as coordinates
Two clock faces with a red curved arrow on each: the first turns the way the hands move and is labelled clockwise, the second turns against them and is labelled anticlockwise
Source: Rotations by Save My Exams
  • Half turns need no direction, since 180° clockwise and anticlockwise give the same image
  • Mark schemes accept equivalents such as 270° clockwise for 90° anticlockwise, and abbreviations like acw