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Enlargement - 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
Enlargement
Transformations and constructions
Lesson 3 of 8
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Warm-up
Transformations and constructions
Lesson 3 of 8
Answer each one, then check.
1
What is 3 × 4?
2
Work out ½ × 8.
3
What is the area of a rectangle 3 by 5?
4
What is the scale factor from 4 cm to 12 cm?
5
What does congruent mean?
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Warm-up - Answers
Transformations and constructions
Lesson 3 of 8
1
What is 3 × 4?
12
2
Work out ½ × 8.
4
3
What is the area of a rectangle 3 by 5?
15
4
What is the scale factor from 4 cm to 12 cm?
3
5
What does congruent mean?
The same shape and size
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Learning Objectives
Transformations and constructions
Lesson 3 of 8
1
Enlarge a shape by a positive scale factor from a centre.
2
Use fractional scale factors.
3
Describe an enlargement fully.
4
Use negative scale factors and similar-shape area and volume ratios (Higher).
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Transformations and constructions
Lesson 3 of 8
THE KEY IDEA
An enlargement changes the size of a shape but not its shape: every length is multiplied by the scale factor.
The centre of enlargement stays in the same place.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Enlarging from a Centre
Transformations and constructions
Lesson 3 of 8
Lines through matching points all meet at the centre of enlargement.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
How to Enlarge a Shape
Transformations and constructions
Lesson 3 of 8
Work from the centre to each vertex.
1
Pick the centre
It is given, or found where lines through matching points meet.
2
Measure to a vertex
Count squares across and up from the centre.
3
Multiply by the scale factor
Multiply both distances.
4
Plot the new vertex
Start again from the centre.
5
Join up
Join the new vertices to make the image.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Enlarging from the Origin
Transformations and constructions
Lesson 3 of 8
Triangle A has vertices (1, 1), (3, 1) and (1, 2). Enlarge it by scale factor 2 with centre (0, 0).
1
Multiply each coordinate by 2
(1, 1) → (2, 2)
2
The other vertices
(3, 1) → (6, 2) and (1, 2) → (2, 4)
ANSWER
The image has vertices (2, 2), (6, 2) and (2, 4).
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Enlarging from Another Centre
Transformations and constructions
Lesson 3 of 8
A triangle has vertices (2, 2), (4, 2) and (2, 3). Enlarge it by scale factor 2 about the centre (1, 1).
1
Vector from the centre to the first vertex
(2, 2) − (1, 1) = (1, 1)
2
Multiply by 2
(2, 2)
3
Add back to the centre
(1 + 2, 1 + 2) = (3, 3)
4
The other vertices
(4, 2): vector (3, 1), doubled (6, 2), so (7, 3); (2, 3): vector (1, 2), doubled (2, 4), so (3, 5)
ANSWER
The image has vertices (3, 3), (7, 3) and (3, 5).
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
A Fractional Scale Factor
Transformations and constructions
Lesson 3 of 8
Enlarge the triangle with vertices (2, 4), (6, 4) and (2, 8) by scale factor ½ with centre (0, 0).
1
Multiply each coordinate by ½
(2, 4) → (1, 2)
2
The other vertices
(6, 4) → (3, 2) and (2, 8) → (1, 4)
ANSWER
The image has vertices (1, 2), (3, 2) and (1, 4); it is smaller than the original.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Scale Factor Sizes
Transformations and constructions
Lesson 3 of 8
SCALE FACTOR GREATER THAN 1
• The image is bigger than the object.
• Lengths are multiplied by the scale factor.
• Example: scale factor 3 makes every side three times as long.
SCALE FACTOR BETWEEN 0 AND 1
• The image is smaller than the object.
• Still called an enlargement.
• Example: scale factor ½ halves every length.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
HIGHER TIER
Negative Scale Factors and Similar Shapes
Enlarge through the centre, and how area and volume scale.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Higher
A Negative Scale Factor
Transformations and constructions
Lesson 3 of 8
Enlarge the point (1, 2) by scale factor −2 about the origin.
1
Multiply the coordinates by −2
(1, 2) → (−2, −4)
2
The image is on the opposite side of the centre
And twice as far away
ANSWER
(−2, −4)
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Higher
Lengths, Areas and Volumes
Transformations and constructions
Lesson 3 of 8
For similar shapes with length scale factor k.
Measurement
Scale factor
Lengths
k
Areas
k²
Volumes
k³
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Higher
Area and Volume Scale Factors
Transformations and constructions
Lesson 3 of 8
Two similar bottles have heights 6 cm and 9 cm. The label of the smaller bottle has area 20 cm². Find the label area on the larger bottle. The smaller bottle holds 250 ml; find the capacity of the larger.
1
Length scale factor
9 ÷ 6 = 1.5
2
Area scale factor
1.5² = 2.25, so 20 × 2.25 = 45
3
Volume scale factor
1.5³ = 3.375, so 250 × 3.375 = 843.75
ANSWER
Label area 45 cm² and capacity 843.75 ml.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Key Terms
Transformations and constructions
Lesson 3 of 8
Enlargement
A transformation that changes the size of a shape by a scale factor.
Scale factor
The number every length is multiplied by.
Centre of enlargement
The fixed point the enlargement is measured from.
Similar
The same shape but a different size.
Ray
A straight line drawn from the centre through a vertex.
Congruent
The same shape and size.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Transformations and constructions
Lesson 3 of 8
YOUR TASK
Describe the Enlargement
12 minutes
Triangle P has vertices (2, 1), (4, 1) and (2, 4). Triangle Q has vertices (4, 2), (8, 2) and (4, 8). Describe fully the single transformation that maps P onto Q. Then find the ratio of their areas.
1
Compare corresponding side lengths.
2
Draw rays to find the centre.
3
Compare areas.
WHAT A GOOD ANSWER SHOWS
Enlargement, scale factor 2, centre (0, 0). The area of P is 3 and the area of Q is 12, a ratio of 1:4, which is 2².
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Can I...?
Transformations and constructions
Lesson 3 of 8
Enlarge from the origin.
Enlarge from another centre.
Use a fractional scale factor.
Describe an enlargement fully.
Find the centre using rays.
Use a negative scale factor (Higher).
Use k² for areas (Higher).
Use k³ for volumes (Higher).
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Summary & Exam Focus
Every length is multiplied by the scale factor.
Scale factors below 1 make the image smaller.
To describe: enlargement, scale factor, centre.
Higher: areas scale by k² and volumes by k³.
EXAM FOCUS
Describe fully the single transformation that maps triangle P onto triangle Q, where P has vertices (2, 1), (4, 1), (2, 4) and Q has vertices (4, 2), (8, 2), (4, 8). (3 marks)
For an enlargement give three things: the word enlargement, the scale factor, and the centre.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Enlargement
Transformations and constructions
Lesson 3 of 8
Answer all questions. Show your working. · 25 minutes
Question 1 · 2 marks · Non-calculator
Triangle A has vertices (1, 1), (3, 1) and (1, 2). It is enlarged by scale factor 2 with centre (0, 0). Write down the coordinates of the…
Question 2 · 2 marks · Non-calculator
A rectangle measures 3 cm by 5 cm. It is enlarged by scale factor 4. Write down the dimensions of the enlarged rectangle.
Question 3 · 3 marks · Non-calculator
A triangle has vertices (2, 2), (4, 2) and (2, 3). It is enlarged by scale factor 2 with centre (1, 1). Write down the coordinates of the…
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Enlargement (cont.)
Transformations and constructions
Lesson 3 of 8
Question 4 · 3 marks · Non-calculator
Triangle Q is an enlargement of triangle P. Describe fully the single transformation that maps P onto Q.
Question 5 · 3 marks · Non-calculator
Two similar vases have heights 6 cm and 9 cm. The surface area of the smaller vase is 20 cm². Work out the surface area of the larger vase.
Question 6 · 3 marks · Calculator
A model of a ship is made to a scale of 1 : 5. The volume of the model is 250 cm³. Work out the volume of the real ship in cm³.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 1 · 2 marks · Non-calculator
Transformations and constructions
Lesson 3 of 8
“
Triangle A has vertices (1, 1), (3, 1) and (1, 2). It is enlarged by scale factor 2 with centre (0, 0). 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 3 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 · 2 marks · Non-calculator
Transformations and constructions
Lesson 3 of 8
“
A rectangle measures 3 cm by 5 cm. It is enlarged by scale factor 4. Write down the dimensions of the enlarged rectangle.
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 2 · mark scheme
Transformations and constructions
Lesson 3 of 8
2 marks available. Award a mark for each point made.
One length correct
M1
Both correct
A1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 3 · 3 marks · Non-calculator
Transformations and constructions
Lesson 3 of 8
“
A triangle has vertices (2, 2), (4, 2) and (2, 3). It is enlarged by scale factor 2 with centre (1, 1). Write down the coordinates of the vertices of the image.
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 3 · mark scheme
Transformations and constructions
Lesson 3 of 8
3 marks available. Award a mark for each point made.
A correct method: vector from the centre doubled
M1
Two vertices correct
A1
All three correct
A1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 4 · 3 marks · Non-calculator
Transformations and constructions
Lesson 3 of 8
Triangle Q is an enlargement of triangle P. Describe fully the single transformation that maps P onto Q. (3 marks)
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 4 · mark scheme
Transformations and constructions
Lesson 3 of 8
3 marks available. Award a mark for each point made.
Enlargement
B1
Scale factor 2
B1
Centre (0, 0)
B1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 5 · 3 marks · Non-calculator
Transformations and constructions
Lesson 3 of 8
“
Two similar vases have heights 6 cm and 9 cm. The surface area of the smaller vase is 20 cm². Work out the surface area of the larger vase.
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 3 of 8
3 marks available. Award a mark for each point made.
Length scale factor 1.5
M1
1.5²
M1
45
A1
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Question 6 · 3 marks · Calculator
Transformations and constructions
Lesson 3 of 8
“
A model of a ship is made to a scale of 1 : 5. The volume of the model is 250 cm³. Work out the volume of the real ship in cm³.
HOW TO ANSWER IT
Command word: 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 3 of 8
3 marks available. Award a mark for each point made.
Length scale factor 5
M1
5³ = 125
M1
31 250
A1
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