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

A real life use of this is

An excellent real-life example of translation is the movement of an aircraft as it moves over the skies. Moving a tangram on a flat surface is also a translation.

this kind of use vectors

Reflections

What is a reflection?

• A reflection is a mirror image of an object across a line of reflection/mirror line

• The reflected image  is the same shape and size as the original object but it has been "flipped" across the mirror line to a new position and orientation

• Points on the mirror line do not move, they stay where they are!

How do I reflect a shape?

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

• The perpendicular distance between a point on the original object and the mirror line, should be the same as the perpendicular distance between the corresponding point on the reflected image and the mirror line

very easy way to learn this thin the line as the mirror and then flip and paste it on the other side like looking at a mirror

How do I describe a reflection?

• You will need to be able to identify and describe a reflection when presented with one

• You must fully describe a transformation to get full marks

  
  

• For a reflection, you must:

  • State that the transformation is a reflection

  • Give the mathematical equation of the mirror line

Now the vector i told is basically the math formula so it is easy

Rotations

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

now this is too easy first take a paper then draw a shape then you choose a point. then take a pencil and push on the paper on the point and rotate the paper by what ever angle using an protractor .

and in exam, you have to say which direction by saying anti-clockwise or clockwise

Enlargements

What is an enlargement?

• An enlargement is a transformation that changes the size of the shape

  • The scale factor tells you how many times bigger each edge of the enlarged image will be compared to the corresponding edge on the original object

  • If the scale factor is greater than 1, the enlarged image will be bigger than the original object

  • If the scale factor is less than 1, the enlarged image will be smaller than the original object

• The position of a shape will also change with enlargement

• The orientation of the shape will be the same for a positive enlargement

this is size but still there will be points to draw it from but no vectors for this one