Reflections (Edexcel GCSE Maths): Revision Notes
Reflections
What is a reflexion?
A reflexion is a transformation where a shape is flipped over a mirror line to create an identical image on the opposite side. When you reflect a shape, you are essentially creating its mirror image across a specific line.
The mirror line acts as a line of symmetry - if you were to fold the paper along this line, the original shape and its reflexion would match up perfectly.
Key properties of reflections
Reflected shapes are congruent - this means the original shape and its reflexion are exactly the same size and shape, just in different positions.
To properly describe a reflexion in your exam, you must state the equation of the mirror line. Simply saying "reflexion" is not enough - you need to specify exactly where the mirror line is located.
Common mirror lines
You'll encounter several types of mirror lines in your exams:
- Vertical lines like (a vertical line passing through )
- Horizontal lines like the x-axis ()
- The y-axis ()
- Diagonal lines like
How to reflect shapes using tracing paper
Practical Method: Using Tracing Paper for Reflections
This method helps you check your work and create accurate reflections:
- Trace the original shape including the mirror line onto tracing paper
- Turn the diagram so the mirror line becomes vertical if it isn't already
- Flip the tracing paper over, lining up the mirror lines
- Turn the paper back to its original orientation
This method is particularly useful for checking your answers and ensuring accuracy.
Describing reflections in exams
When describing a reflexion, you must be specific about the mirror line. The examiners expect you to:
- Write "reflexion" to identify the transformation type
- State the mirror line clearly - if it's a coordinate axis, write it out fully rather than just giving the equation
- Be precise - saying "reflexion in the y-axis" is safer than "reflexion in "
Exam tips
- Always label reflected shapes with the letters given in the question
- Check your work by ensuring the original and reflected shapes are the same distance from the mirror line
- Use grid lines to help count squares and maintain accuracy
- Practice identifying different types of mirror lines on coordinate grids
Key Points to Remember:
- Reflections create mirror images across a specified line
- Reflected shapes are always congruent to the original
- You must state the mirror line equation when describing reflections
- Tracing paper is a reliable method for creating and checking reflections
- Be specific about mirror lines in exam answers - write them out clearly