What are transformations in maths?

• There are 4 transformations in GCSE Maths – rotation, reflection, translation and enlargement
• All 4 change a shape in some way, useful in things like computer graphics.
• There is some language and notation often used in this topic – the original shape is called the object and the transformed shape is called the image
• Vertices are labelled to show corresponding points
  • Vertices on the object are labelled A, B, C, etc.
  • Vertices on the image are labelled A’, B’, C’ etc.
  • If there is a second transformation then they will become A”, B”, C” etc.

What is a translation?

• A translation is the movement of a shape
• The size, shape and orientation (which way up it is) of the shape stays the same

 

How do I translate a shape?

• The movement of a translation is described by a vector
• You need to know how to write a translation using a vector (rather than words)
• Vectors are written as column vectors in the form  where:
  • is the distance moved horizontally
    • Negative means move to the left
    • Positive means move to the right
  • is the distance moved vertically
    • Negative means move down
    • Positive means move up

• STEP 1:

  Select a vertex on the original object, move it according to the information given in the column vector

• STEP 2:

  Repeat STEP 1 for each of the vertices on the original object

• STEP 3:
  Connect the translated vertices and label the translated image
  
  
• In some cases, where the vectors are small enough, the image can overlap the object
• The vector is how the shape moves not the size of the gap between the object and the image, watch out for this common error!

 

How do I describe a translation?

• It is important to fully describe a transformation in order to get full marks
• For a translation, you must:
  • State that the transformation is a translation
  • Give the column vector that describes the movement

  

Which points are invariant with a translation?

• Invariant points are points that do not change position when a transformation has been performed
  • Invariant points don't move!
• With a translation, there are no invariant points, as all points are translated with the object