What is a rotation?

• A rotation is the movement of an object around a point
• The rotated image is the same size and shape as the original image, but it will have a new position and orientation

How do I rotate a shape?

• You need to be able to perform a rotation (on a coordinate grid)

• The easiest way to draw a rotation is to use tracing paper, this should be available to you in an exam but you may have to ask an invigilator for it

• 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 the angle that has been asked for in the question, it will usually be an "easy" angle such as 90 ^o, 180 ^o or 270 ^o

• STEP 4:
  Your tracing paper is in the position showing you where to draw the rotated image, carefully draw the image onto the coordinate grid

How do I describe a rotation?

• You will need to be able to identify and describe a rotation when presented with one
• You must fully describe a transformation to get full marks
• For a rotation you must:
  • State that the transformation is a rotation
  • State the centre of rotation (the point about which the object is rotated)
  • State the angle of rotation (how many degrees around the point that the object has been rotated)
  • State the direction of rotation (clockwise or anticlockwise, unless the angle is 180 ^o, then a direction is not required)

Which points are invariant with a rotation?

• Invariant points are points that do not change position when a transformation has been performed
  • Invariant points don't move!
• With a rotation, if the centre of rotation is a  point on  the object, then that point is invariant
  • if the centre of rotation is not a point on the object, then there are no invariant points
• Rotating an object by 360° (or any multiple of 360) means it returns back to its original position
  • all points on the object are invariant in this case 
  • be careful: rotating a rectangle by 180° about its centre might look like the rectangle hasn't changed, but individual points have moved position (so they're not invariant)