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Reflection and rotation - Teacher Slides.pptx
The lesson slides with the teacher's notes on each slide, and every question and mark scheme built in. Built from the lesson script on 30 September 2026.
EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Reflection and rotation
Transformations and constructions
Lesson 2 of 8
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Warm-up
Transformations and constructions
Lesson 2 of 8
Answer each one, then check.
1
What are the coordinates of the origin?
2
What is the equation of the y-axis?
3
What is the equation of the x-axis?
4
How many degrees in a half turn?
5
What is the reflection of (2, 3) in the y-axis?
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Warm-up - Answers
Transformations and constructions
Lesson 2 of 8
1
What are the coordinates of the origin?
(0, 0)
2
What is the equation of the y-axis?
x = 0
3
What is the equation of the x-axis?
y = 0
4
How many degrees in a half turn?
180
5
What is the reflection of (2, 3) in the y-axis?
(−2, 3)
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Learning Objectives
Transformations and constructions
Lesson 2 of 8
1
Reflect a shape in a mirror line, including y = x.
2
Rotate a shape about a centre through 90° or 180°.
3
Describe a reflection fully.
4
Describe a rotation fully.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Congruent Transformations
Transformations and constructions
Lesson 2 of 8
Object and image
The original shape is the object; the shape after the transformation is the image.
Congruent
Reflection and rotation keep the size and shape the same, so the image is congruent to the object.
Orientation
A reflection flips the shape; a rotation turns it.
Describe fully
Name the transformation and give all the details needed.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
A Reflection and a Rotation
Transformations and constructions
Lesson 2 of 8
Each point of the image is the same distance from the mirror line, or the same distance from the centre of rotation.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Reflection or Rotation?
Transformations and constructions
Lesson 2 of 8
REFLECTION
• Flips the shape over a mirror line.
• Each point and its image are the same distance from the line, on opposite sides.
• Describe with the equation of the mirror line, e.g. x = 4, y = x.
ROTATION
• Turns the shape about a fixed point, the centre.
• Each point and its image are the same distance from the centre.
• Describe with the angle, the direction (clockwise or anticlockwise) and the centre.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Reflecting in a Line
Transformations and constructions
Lesson 2 of 8
Triangle A has vertices (1, 1), (1, 3) and (3, 1). Reflect it in the line x = 4.
1
Each point is 3, 3 and 1 away from the line x = 4 horizontally
(1, 1) is 3 to the left
2
Go the same distance to the right of the line
(7, 1)
3
Do the same for the other vertices
(1, 3) → (7, 3) and (3, 1) → (5, 1)
ANSWER
The image has vertices (7, 1), (7, 3) and (5, 1).
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Rotating About the Origin
Transformations and constructions
Lesson 2 of 8
Rotate triangle A, with vertices (1, 1), (1, 3) and (3, 1), through 90° clockwise about the origin.
1
Rule for 90° clockwise about the origin
(x, y) → (y, −x)
2
Apply it
(1, 1) → (1, −1)
3
The other vertices
(1, 3) → (3, −1) and (3, 1) → (1, −3)
ANSWER
The image has vertices (1, −1), (3, −1) and (1, −3).
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Describing a Rotation
Transformations and constructions
Lesson 2 of 8
Triangle A has vertices (1, 1), (1, 3) and (3, 1). Triangle B has vertices (−1, −1), (−1, −3) and (−3, −1). Describe fully the single transformation that maps A onto B.
1
The shape has turned upside down
A half turn
2
Each x and y has changed sign
Centre at the origin
3
Name the transformation with the three details
Rotation, 180°, centre (0, 0)
ANSWER
A rotation of 180° about the centre (0, 0).
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Quick Rules About the Origin
Transformations and constructions
Lesson 2 of 8
Handy for checking your answers.
Transformation
Rule for (x, y)
Reflection in the y-axis
(−x, y)
Reflection in the x-axis
(x, −y)
Reflection in y = x
(y, x)
Rotation 90° clockwise
(y, −x)
Rotation 90° anticlockwise
(−y, x)
Rotation 180°
(−x, −y)
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Key Terms
Transformations and constructions
Lesson 2 of 8
Object
The original shape before a transformation.
Image
The shape after a transformation.
Congruent
The same shape and size, possibly turned or flipped.
Mirror line
The line a shape is reflected in.
Centre of rotation
The fixed point a shape turns about.
Clockwise
The direction the hands of a clock move.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Transformations and constructions
Lesson 2 of 8
YOUR TASK
Transformation Detective
12 minutes
Triangle A has vertices (1, 1), (1, 3) and (3, 1). Work out the vertices of its image under (a) reflection in the x-axis (b) reflection in y = x (c) rotation 90° anticlockwise about the origin. Then say which of the three images touches the original at a point.
1
Apply the rule.
2
Plot the image.
3
Check distances from the mirror line.
WHAT A GOOD ANSWER SHOWS
(a) (1, −1), (1, −3), (3, −1). (b) (1, 1), (3, 1), (1, 3), which is the same triangle. (c) (−1, 1), (−3, 1), (−1, 3). Image (b) coincides with A because A is symmetrical about y = x.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Can I...?
Transformations and constructions
Lesson 2 of 8
Reflect in the axes.
Reflect in a line such as x = 4.
Reflect in y = x.
Rotate about the origin.
Rotate about another point.
Describe a reflection fully.
Describe a rotation fully.
Use the rules for coordinates.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Summary & Exam Focus
Reflection: name it and give the mirror line equation.
Rotation: give the angle, the direction and the centre.
Distances from the mirror line or the centre are preserved.
Rotations and reflections keep the shape congruent.
EXAM FOCUS
Describe fully the single transformation that maps triangle P onto triangle Q, where the vertices of P are (1, 1), (1, 3), (3, 1) and the vertices of Q are (7, 1), (7, 3), (5, 1). (3 marks)
A full description needs the name of the transformation and all its details: for a reflection, the equation of the mirror line.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Reflection and Rotation
Transformations and constructions
Lesson 2 of 8
Answer all questions. Show your working. · 25 minutes
Question 1 · 2 marks · Non-calculator
Triangle A has vertices (1, 1), (1, 3) and (3, 1). It is reflected in the y-axis. Write down the coordinates of the vertices of the image.
Question 2 · 3 marks · Non-calculator
Triangle A has vertices (1, 1), (1, 3) and (3, 1). Triangle B has vertices (−1, −1), (−1, −3) and (−3, −1). Describe fully the single…
Question 3 · 3 marks · Non-calculator
The diagram shows triangles P and Q on a grid. Describe fully the single transformation that maps triangle P onto triangle Q.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Reflection and Rotation (cont.)
Transformations and constructions
Lesson 2 of 8
Question 4 · 2 marks · Non-calculator
The point (2, 5) is reflected in the line y = x. Write down the coordinates of the image.
Question 5 · 3 marks · Non-calculator
The point P(3, 1) is rotated 90° anticlockwise about the origin. Write down the coordinates of the image of P.
Question 6 · 3 marks · Non-calculator
The point P(4, 2) is rotated 90° clockwise about the point C(2, 1). Find the coordinates of the image of P.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 1 · 2 marks · Non-calculator
Transformations and constructions
Lesson 2 of 8
“
Triangle A has vertices (1, 1), (1, 3) and (3, 1). It is reflected in the y-axis. Write down the coordinates of the vertices of the image.
HOW TO ANSWER IT
Command word: Non-calculator. Worth 2 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 1 · mark scheme
Transformations and constructions
Lesson 2 of 8
2 marks available. Award a mark for each point made.
Two vertices correct
B1
All three correct
B1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 2 · 3 marks · Non-calculator
Transformations and constructions
Lesson 2 of 8
“
Triangle A has vertices (1, 1), (1, 3) and (3, 1). Triangle B has vertices (−1, −1), (−1, −3) and (−3, −1). Describe fully the single transformation that maps triangle A onto triangle B.
HOW TO ANSWER IT
Command word: Non-calculator. Worth 3 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 2 · mark scheme
Transformations and constructions
Lesson 2 of 8
3 marks available. Award a mark for each point made.
Rotation
B1
180°
B1
Centre (0, 0)
B1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 3 · 3 marks · Non-calculator
Transformations and constructions
Lesson 2 of 8
The diagram shows triangles P and Q on a grid. Describe fully the single transformation that maps triangle P onto triangle Q. (3 marks)
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 3 · mark scheme
Transformations and constructions
Lesson 2 of 8
3 marks available. Award a mark for each point made.
Reflection
B1
The line x = 4
B2
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 4 · 2 marks · Non-calculator
Transformations and constructions
Lesson 2 of 8
“
The point (2, 5) is reflected in the line y = x. Write down the coordinates of the image.
HOW TO ANSWER IT
Command word: Non-calculator. Worth 2 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 4 · mark scheme
Transformations and constructions
Lesson 2 of 8
2 marks available. Award a mark for each point made.
One coordinate correct
M1
(5, 2)
A1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 5 · 3 marks · Non-calculator
Transformations and constructions
Lesson 2 of 8
“
The point P(3, 1) is rotated 90° anticlockwise about the origin. Write down the coordinates of the image of P.
HOW TO ANSWER IT
Command word: Non-calculator. Worth 3 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 5 · mark scheme
Transformations and constructions
Lesson 2 of 8
3 marks available. Award a mark for each point made.
A correct rotation method
M1
One coordinate correct
A1
(−1, 3)
A1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 6 · 3 marks · Non-calculator
Transformations and constructions
Lesson 2 of 8
“
The point P(4, 2) is rotated 90° clockwise about the point C(2, 1). Find the coordinates of the image of P.
HOW TO ANSWER IT
Command word: Non-calculator. Worth 3 marks, so plan before writing.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 6 · mark scheme
Transformations and constructions
Lesson 2 of 8
3 marks available. Award a mark for each point made.
Vector from C to P is (2, 1)
M1
Rotated vector (1, −2)
M1
(3, −1)
A1
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