GCSE MATHS • HIGHER TIER
Reflections Made Simple
Reflect points, shapes and graphs accurately across axes and other mirror lines.
Clear method
Exam practice
Worked proofs
Reflections in Four Moves
1
Identify
Identify the mirror line or axis of reflection.
2
Measure
Find the perpendicular distance from each point to the mirror line.
3
Reflect
Place the image the same distance on the opposite side.
4
Check
Confirm that the reflected image has the same size and shape and is a true mirror image.
What You’ll Learn
Understand what a reflection is.
Recognise common lines of reflection.
Reflect points in the x-axis and y-axis.
Reflect points in other horizontal and vertical lines.
Understand reflections of graphs.
Avoid common coordinate and mirror-line mistakes.
Key Rules
x-axis reflection
(x, y) → (x, −y)
y-axis reflection
(x, y) → (−x, y)
Mirror line rule
Every point stays the same perpendicular distance from the mirror line.
Shape rule
A reflection keeps the same size & shape but creates a mirror image.
Worked Proof: Reflections
Step-by-Step Method
- 1. Identify the mirror line or axis.
- 2. Find the perpendicular distance from each point to the mirror line.
- 3. Place each point the same distance on the opposite side.
- 4. Join the reflected points if reflecting a complete shape.
- 5. Check that the new shape is the same size and shape and forms a true mirror image.
More Worked Examples
1
Reflecting in the x-axis
Reflect (5, 2) in the x-axis.
Step 1: Keep the x-coordinate.
x = 5
Step 2: Change the sign of y.
2 becomes -2
x = 5
Step 2: Change the sign of y.
2 becomes -2
2
Reflecting in the y-axis
Reflect (7, 3) in the y-axis.
Step 1: Change the sign of x.
7 becomes -7
Step 2: Keep the y-coordinate.
y = 3
7 becomes -7
Step 2: Keep the y-coordinate.
y = 3
3
Reflecting in Other Vertical Lines
Reflect the point (5, 4) in the line x = 2.
Step 1: Count the distance from x = 2.
5 is 3 units right of x = 2
Step 2: Move 3 units to the opposite side.
2 - 3 = -1
Step 3: Keep the y-coordinate.
y = 4
5 is 3 units right of x = 2
Step 2: Move 3 units to the opposite side.
2 - 3 = -1
Step 3: Keep the y-coordinate.
y = 4
4
Reflecting in Other Horizontal Lines
Reflect (3, 7) in the line y = 4.
Step 1: Count the vertical distance.
7 is 3 units above y = 4
Step 2: Move 3 units below.
4 - 3 = 1
Step 3: Keep the x-coordinate.
x = 3
7 is 3 units above y = 4
Step 2: Move 3 units below.
4 - 3 = 1
Step 3: Keep the x-coordinate.
x = 3
- Common GCSE Mistakes
- Moving points unequal distances.
- Reflecting across the wrong axis.
- Forgetting which coordinate changes.
- Miscounting distances from mirror lines.
- Confusing reflections with translations.
- Exam Tips
- Identify the mirror line before moving any point.
- Remember: reflection in the x-axis changes y.
- Remember: reflection in the y-axis changes x.
- Keep every point the same perpendicular distance from the mirror line.
- Reflect each vertex separately when transforming a shape.
- Check that the final image has the same size and shape as the original.
Skills Used in Reflections
Reflections
Coordinates
Symmetry
Mirror Lines
Transformations
Graph Transformations
Ready to Practise?
Printable Worksheet
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Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Reflections Tutorial
Step-by-step walkthroughs of Reflections with clear methods and exam tips.
Frequently Asked Questions
A reflection flips a shape over a mirror line to create a mirror image.
The x-coordinate stays the same and the y-coordinate changes sign.
The y-coordinate stays the same and the x-coordinate changes sign.
Measure the horizontal distance to x = 2 and place the image the same distance on the opposite side.
Reflect each vertex individually and then join the new vertices.
The shape, size and perpendicular distance from the mirror line.