Translations (Edexcel GCSE Maths): Revision Notes
Translations
What is a translation?
A translation is a type of transformation where a shape slides from one position to another without rotating or changing size. Think of it like sliding a book across a table - the book stays exactly the same, it just moves to a different position.
The key characteristic of translation is that the shape maintains its size, orientation, and angles - it simply changes position in space.
You can describe any translation precisely using a vector, which tells you exactly how far and in which direction the shape has moved.
Vector notation
Vectors are written in a special format that shows two pieces of information about the movement:
Vector format:
The top number tells you the horizontal movement:
- Positive number = movement to the right
- Negative number = movement to the left
The bottom number tells you the vertical movement:
- Positive number = movement up
- Negative number = movement down
Worked Example: Reading Vector Notation
The vector means:
- Move 4 units to the right (positive horizontal)
- Move 3 units down (negative vertical)
Properties of translated shapes
When you translate a shape, the new shape is congruent to the original. This means the translated shape maintains all its essential properties:
Congruent shapes have:
- All side lengths stay the same
- All angles stay the same
- Only the position changes
Describing translations fully
To get full marks when describing a translation, you must include both essential components:
Required for Full Marks:
- Write the word "translation"
- State the vector using the correct notation
Example: "Translation by the vector "
Exam Tip: Don't use the word "across" to describe translations, as this could mean movement in either direction. Always use vectors to be precise and avoid losing marks.
Working with translation problems
When you're asked to find a translation vector, follow this systematic approach:
- Count the horizontal movement first (left/right)
- Then count the vertical movement (up/down)
- Remember your signs: right and up are positive, left and down are negative
- Write your answer as where x is horizontal and y is vertical
Key Points to Remember:
- Translation = sliding movement with no rotation or size change
- Use vector notation to describe translations precisely
- Positive numbers mean right/up, negative numbers mean left/down
- Translated shapes are congruent - same size and shape, different position
- Always write "Translation by the vector..." for full marks in exams