Rotation

A rotation is a transformation where a point, or an object, is turned around a fixed point to a new LondonEyeBig.JPGposition called the image.

The object and the image are the same shape and the same size but in different positions.

When a shape or point is rotated there is acentre of rotation which remains fixed.

The angle of rotation gives the number of degrees that the shape is rotated through.

The direction of rotation is either clockwise oranti-clockwise.
Clockwise rotations are given by a NEGATIVEangle.
Anti-clockwise rotations are given by aPOSITIVE angle.

If the angle of rotation is 90° the rotation is called a QUARTER turn.

If the angle of rotation is 180° the rotation is called a HALF turn.

The diagram shows a rotation of 90° clockwise (-90°) about the centre of rotation, O.

Y8_Rotation_02.gif
 

Properties of Rotation

Triangle PQR maps to triangle P´Q´R´ under a rotation of 90°, anti-clockwise, centre O.

Y8_Rotation_03.gif

 

  • All points and lines, except the centre, turn through an angle of 90°

    e.g. Y8_Rotation_04.gifPOP´ = Y8_Rotation_04.gifQOQ´ = Y8_Rotation_04.gif ROR´ = 90°

  • Length, angle size and area are invariant.

    e.g. length PQ = length P´Q´

    • Y8_Rotation_04.gifPQR = Y8_Rotation_04.gifP´Q´R´

      area Y8_Rotation_05.gif PQR = area Y8_Rotation_05.gif P´Q´R´

  • The centre of rotation, O, is the only invariant point.

To see examples of rotations − Y8_Rotation_06.gif

Drawing a Rotation

 

Y8_Rotation_07.gif

Sometimes the centre of rotation can actually be on the object itself.