GCSE MATHS • HIGHER TIER
Reflection Made Simple
Reflect points and shapes accurately across axes and other mirror lines using equal distances.
Clear method
Exam practice
Worked proofs
Reflection in Four Moves
1
Identify
Find the mirror line or line of reflection.
2
Measure
Check each vertex or point’s perpendicular distance from the mirror line.
3
Reflect
Place the image the same distance on the opposite side of the mirror line.
4
Plot and Join
Plot reflected points accurately and join them to complete the image.
What You’ll Learn
Understand what a reflection is.
Recognise key features of reflections.
Reflect points in the x-axis and y-axis.
Reflect points in lines such as x = 2 and y = 5.
Reflect complete shapes using equal distances.
Describe a reflection using its mirror line.
Key Rules
Mirror line
A reflection flips a shape across a mirror line while keeping the same size & shape.
Equal distance
Every point must be the same perpendicular distance from the mirror line on the opposite side.
Reflection in x-axis
(x, y) → (x, −y) — keep x the same & change the sign of y.
Reflection in y-axis
(x, y) → (−x, y) — keep y the same & change the sign of x.
Worked Proof: Reflection
Step-by-Step Method
- 1. Find the radius or diameter.
- 2. Calculate the circumference..
- 3. Find the fraction represented by the angle.
- 4. Multiply the circumference by this fraction. the angle.
- 5. Give the answer in exact or decimal form.
More Worked Examples
1
Reflection in the y-axis
Reflect the point (6, -2) in the y-axis.
(6, -2) → (-6, -2)
2
Reflect the point (4, 8) in the line y = 5.
The point is 3 units above y = 5.
Move 3 units below.
3
Reflect the point (5, 2) in the y-axis.
The x-coordinate becomes -5.
The y-coordinate remains 2.
4
Reflect the point (5, 3) in the line x = 2.
The point is 3 units to the right of x = 2.
Move 3 units to the left.
- Common GCSE Mistakes
- Reflecting across the wrong axis.
- Counting distances incorrectly.
- Forgetting equal distance from the mirror line.
- Confusing reflections with translations.
- Changing both coordinates when only one should change.
- Exam Tips
- Draw or identify the mirror line clearly.
- For x-axis reflections, change only the sign of y.
- For y-axis reflections, change only the sign of x.
- Keep every point the same perpendicular distance from the mirror line.
- Reflect each vertex separately before joining the shape.
- When describing a reflection, always state the line of reflection.
Skills Used in Reflection
Transformations
Coordinates
Mirror Lines
Spatial Awareness
Reflectional Symmetry
Accurate Plotting
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Reflection Tutorial
Step-by-step walkthroughs of Reflection with clear methods and exam tips.
Frequently Asked Questions
A reflection flips a shape across a mirror line while keeping its size and shape unchanged.
The x-coordinate stays the same and the y-coordinate changes sign.
The y-coordinate stays the same and the x-coordinate changes sign.
Count the perpendicular distance to the mirror line and place the image the same distance on the opposite side.
State that it is a reflection and give the line of reflection.
No. The reflected image has exactly the same size and shape as the original.