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Translations (Edexcel IGCSE Maths)
Revision Note
Translations
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
- is the distance moved horizontally
- 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
Examiner Tip
- Translate one vertex of the shape at a time, put your pencil on the starting position and move across and/up/down the stated number of places and mark the new position of that vertex
- Be careful not to muddle up which points you are translating, it can be surprisingly easy to count the wrong distance, especially if the original object and the translated image overlap each other!
Worked example
The vector means "4 to the left" and "5 up".
You don't have to draw in any arrows but it is a good idea to mark your paper after counting across and up a couple of times to check that you are in the correct place.
Translating one vertex and then following around the shape one vertex at a time makes it easier to get the shape in exactly the right position!
This is a case where the image overlaps the object.
You should still see that the shape is the same size and the same way up so it is a translation.
Start at a vertex on the original object that is well away from any overlap area to avoid confusion and count the number of position left/right and up/down that you need to move to reach the corresponding vertex on the translated image.
Take care when counting around the axes!
Shape A has been translated using the vector
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