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Negative scale factors Quiz

Grade 6 • 6J • 10 Questions (24 Marks)

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Negative scale factors — Notes & Worked Examples Show / Hide

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)
Question 1
[2 marks]
–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 & Answer
(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)
Question Paper (PDF) • Mark Scheme (PDF)
Question 2
[2 marks]
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 & Answer
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)
Question Paper (PDF) • Mark Scheme (PDF)
Question 3
[2 marks]
xy–8–6–4–22468101214–10–8–6–4–2246810O
Enlarge the shaded shape by scale factor –2 with centre of enlargement (0, 0).
Enlarge the shaded shape by scale factor -2 with centre of enlargement (0, 0)
Worked Solution & Answer
Multiply each vertex by –2: (–2, –4)→(4, 8), (–3, –2)→(6, 4), (–5, –2)→(10, 4), (–6, –4)→(12, 8) M1 A1
xy–8–6–4–22468101214–10–8–6–4–2246810O
Answer: Trapezium drawn with vertices (4, 8), (6, 4), (10, 4) and (12, 8)
Question Paper (PDF) • Mark Scheme (PDF)
Question 4
[2 marks]
xy–8–6–4–22468–8–6–4–2246OT
On the grid, enlarge triangle T by scale factor –2 with centre of enlargement (–2, –2).
On the grid, enlarge triangle **T** by scale factor –2 with centre of enlargement (-2, -2)
Worked Solution & Answer
From (–2, –2): (–5, –5) is (–3, –3) ⇒ ×(–2) gives (+6, +6) → (4, 4) M1
(–7, –5) → (8, 4)
(–6, –2) → (6, –2) A1
xy–8–6–4–22468–8–6–4–2246OT
Answer: Triangle drawn with vertices (4, 4), (8, 4) and (6, –2)
Question Paper (PDF) • Mark Scheme (PDF)
Question 5
[2 marks]
xyA–112345678910–112345678910O
Enlarge triangle **A** by scale factor 2.5 with centre (0, 1)
Enlarge triangle **A** by scale factor 2.5 with centre (0, 1)
Worked Solution & Answer
From (0, 1): (1, 1) → (2.5, 1) M1
(1, 3) → (2.5, 1 + 2×2.5) = (2.5, 6)
(2, 3) → (5, 6) A1
xyA–112345678910–112345678910O
Answer: Triangle with vertices at (2.5, 1), (2.5, 6) and (5, 6)
Question Paper (PDF) • Mark Scheme (PDF)
Question 6 AQA Nov 2022 3H Q21
[2 marks]
Shape A is enlarged to shape B.
xyO–6–5–4–3–2–1123456–6–5–4–3–2–1123456AB
(a) Circle the scale factor of the enlargement.
-12 -2 12 2 [1 mark]
(b) Write down the coordinates of the centre of enlargement. [1 mark]
Answer
Worked Solution & Answer
(a)
Base of A is 6 units and inverted base of B is 3 units, so scale factor = –1/2 B1
Answer (a): -12
(b)
Ray through (0, 1) and (0, –2) and ray through (–6, 1) and (3, –2) intersect at (0, –1) B1
Answer (b): Answer 0, -1
Question Paper (PDF) • Mark Scheme (PDF)
Question 7 AQA Nov 2024 1H Q14
[3 marks]
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 & Answer
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)
Question Paper (PDF) • Mark Scheme (PDF)
Question 8 AQA Nov 2019 3H Q24
[3 marks]
Shape A and shape B are shown on the grid.
–5–5–4–4–3–3–2–2–1–11122334455xyOAB
Describe the single transformation that maps shape A to shape B.
Worked Solution & Answer
1. Enlargement (shapes are mathematically similar with different orientations). M1
2. Scale factor: side length of A is 4, side length of B is 2 and inverted ⇒ k = -12 (or -0.5). M1
3. Centre of enlargement: joining corresponding vertices (-5, 5) to (4, -4) and (-1, 5) to (2, -4) gives intersection point (1, -1). A1
Answer: Transformation Enlargement, scale factor -0.5, centre (1, -1)
Question Paper (PDF) • Mark Scheme (PDF)
Question 9 OCR Jun 2025 6H Q19
[3 marks]
Shape **L** is drawn on the grid.
–8–8–7–7–6–6–5–5–4–4–3–3–2–2–1–11122334455667788yx0L
Enlarge shape **L** with scale factor -2 and centre of enlargement at (-1, 2).
Worked Solution & Answer
From centre (−1, 2), multiply each displacement vector by −2: M1
(−4, 2) → (5, 2)
(−2, 2) → (1, 2)
(−2, 3) → (1, 0) M1
(−3, 3) → (3, 0)
(−3, 5) → (3, −4)
(−4, 5) → (5, −4). A1
–8–8–7–7–6–6–5–5–4–4–3–3–2–2–1–11122334455667788yx0L
Answer: Enlarged shape L with vertices (5, 2), (1, 2), (1, 0), (3, 0), (3, −4), (5, −4)
Question Paper (PDF) • Mark Scheme (PDF)
Question 10
[3 marks]
–8–6–4–22468–10–8–6–4–2246OyxP
(a) Enlarge triangle P by scale factor –1.5 with centre (–2, –1). Label your image Q. (2) (b) Triangle P is rotated 90° anticlockwise about O then translated so 1 vertex is invariant. Find one possible column vector. (1)
(a) Enlarge triangle **P** by scale factor -112 with centre of enlargement (-2, -1)
Label your image **Q**. [2 marks]
(b) Find one possible column vector for the translation. [1 mark]
Worked Solution & Answer
(a)
Vectors from (–2, –1) to (–8, 1), (–6, 1), (–8, 5) are (–6, 2), (–4, 2), (–6, 6) M1
multiply by –1.5 to get (9, –3), (6, –3), (9, –9) ⇒ (7, –4), (4, –4), (7, –10) A1
Answer (a): Triangle Q with vertices (7, –4), (4, –4), (7, –10)
(b)
90° anticlockwise sends (x, y) → (–y, x): (–8, 1) → (–1, –8), translation = (–7, 9)
(–6, 1) → (–1, –6), translation = (–5, 7)
(–8, 5) → (–5, –8), translation = (–3, 13) B1
Answer (b): –7, 9
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Score: 0 / 10 (0 / 24 marks)
Negative scale factors Worksheets Next: Circle theorems →

Grade 6 Quizzes

14 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