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Negative scale factors

Free Printable Negative scale factors PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 6)

Download free negative scale factors worksheets (PDF), GCSE maths past paper questions and worked solutions for Negative scale factors (6J). This is a Grade 6 geometry topic from the GCSE questions by topic collection for Higher tier GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Genie, Corbett Maths, Maths Made Easy, 1st Class Maths, Naiker Maths, Metatutor, Maths Takeaway, Dr Austin, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our negative scale factors revision notes and worked examples with diagrams, try real GCSE past paper negative scale factors questions with step-by-step solutions, or download a PDF of all negative scale factors worksheet links.

Free Negative scale factors PDF Worksheets & Answers

Grade 6 • Topic 6J
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Grade 6 topics
6A - Recurring decimals6B - Harder indices
6C - The product rule6D - Repeated change
6E - Triple brackets6F - Parallel and perpendicular
6G - Inequalities on graphs6H - Similar shapes (area and vol)
6J - Negative scale factors6K - Circle theorems
6L - Cumulative frequency6M - Box plots
6N - Combined transformations6P - Capture recapture
GCSE Maths Grade 6 Revision Notes & Method

Guide to Negative scale factors: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

An enlargement with a negative scale factor (−k) enlarges the shape by factor k on the opposite side of the centre of enlargement and turns the image upside down (rotated by 180°).

Count the vector movement (squares across and up/down) from the centre of enlargement to each vertex of the object, multiply that vector by the negative scale factor, and count the new movement from the centre of enlargement.

Example 1: Shape A has a corner at (4, 5). It is enlarged by scale factor −2 about the centre (3, 3). Find the new coordinates of this corner.

(4, 5) (3, 3) (1, −1)

Solution:

From (3, 3) to (4, 5) is (1, 2); multiply by −2 → (−2, −4)
From centre: (3 − 2, 3 − 4) = (1, −1)
Answer: (1, −1)

Example 2: Triangle P (base 2 units) maps onto inverted Triangle Q (base 3 units). Ray lines through matching corners cross at (2, 1). Describe the transformation.

Solution:

1. Transformation type: Enlargement
2. Inverted and 3 ÷ 2 = 1.5 → scale factor −1.5
3. Ray lines intersect at centre (2, 1)
Answer: Enlargement, scale factor −1.5, centre (2, 1)
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Negative scale factors Questions & Answers

Past Paper Example 1 AQA Nov 2024 1H Q14 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
Enlarge triangle PQR by scale factor -13 with centre (0, 0)
–4–3–2–1123456789–4–3–2–1123456789OxyPQR
Enlarge triangle PQR by scale factor –1/3 with centre (0, 0). [3 marks]
Worked Solution & Mark Scheme (3 marks)
Multiply each coordinate by –1/3: M2
P(0, 9) → (0, –3), Q(9, 9) → (–3, –3), R(9, 3) → (–3, –1). A1
–4–3–2–1123456789–4–3–2–1123456789OxyPQR
Answer: Triangle with vertices (0, –3), (–3, –3) and (–3, –1)
Past Paper Example 2 GCSE Nov 2017 1H Q18 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
–8–7–6–5–4–3–2–112345678–8–7–6–5–4–3–2–112345678OxyP
Enlarge shape P by scale factor –1/2 with centre of enlargement (0, 0). Label your image Q.
Enlarge shape **P** by scale factor -12 with centre of enlargement (0, 0).
Label your image **Q**.
Worked Solution & Mark Scheme (2 marks)
(2, 3) → (–1, –1.5) M1
(4, 3) → (–2, –1.5)
(2, 7) → (–1, –3.5) A1
–8–7–6–5–4–3–2–112345678–8–7–6–5–4–3–2–112345678OxyPQ
Answer: Triangle Q with vertices (–1, –1.5), (–2, –1.5) and (–1, –3.5)
Past Paper Example 3 GCSE Jun 2024 3H Q12 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
The diagram shows triangle T drawn on a grid.
xyT–8–7–6–5–4–3–2–112345678–8–7–6–5–4–3–2–112345678O
Enlarge triangle T by scale factor -2 with centre of enlargement (0, 0)
Worked Solution & Mark Scheme (2 marks)
Multiply each vertex of T by –2: (1, 2) → (–2, –4), (3, 2) → (–6, –4), (1, 3) → (–2, –6). M1 A1
xyT–8–7–6–5–4–3–2–112345678–8–7–6–5–4–3–2–112345678O
Answer: Triangle drawn with vertices at (–2, –4), (–6, –4) and (–2, –6)

← 6H Similar shapes (area and vol)

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