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Rotations Quiz

Grade 3 • 3S • 10 Questions (34 Marks)

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Score: 0 / 10
Rotations — Notes & Worked Examples Show / Hide

Explanation:

To describe a rotation fully (3 marks), you must state three things: (1) the word rotation, (2) the angle and direction (90° clockwise, 90° anticlockwise, or 180° — note that 180° does not need a direction), and (3) the coordinates of the centre of rotation.

In the exam, always ask for tracing paper: trace the shape and draw a small arrow pointing North at the centre of rotation, hold your pencil tip firmly on the centre, and turn the tracing paper through the required angle.

Example 1: Point A(1, 4) is rotated 90° clockwise about (0, 0). Find the coordinates of A'.

A(1,4) A'(4,−1) 90°
From (0,0): 1 right, 4 up.
90° CW → 4 right, 1 down.
Answer: (4, −1)

Example 2: Triangle P (2,2), (2,5), (4,2) maps to Q (2,0), (2,−3), (0,0). Describe the transformation.

P Q (2,1)
Turned upside down (180°).
Midpoint of (2,2) & (2,0) is (2, 1).
Rotation, 180°, centre (2, 1)
Question 1
[1 mark]
The point A(1, 2) is rotated 90° clockwise about the origin (0, 0).
Write down the coordinates of the image point A'.
Worked Solution & Answer
Under a 90° clockwise rotation about (0,0), (x, y) → (y, -x) = (2, -1). B1
Answer: (2, -1)
Question 2
[2 marks]
–5–5–4–4–3–3–2–2–1–111223344550xyA
Rotate shape A 180° around (0,0)
Worked Solution & Answer
Mark the centre of rotation and turn each vertex through the given angle and direction.
Vertices at (-2, 4), (-4, 4), (-2, 1)
–5–5–4–4–3–3–2–2–1–111223344550xyAA'
Answer: Vertices at (-2, 4), (-4, 4), (-2, 1)
Question 3
[2 marks]
–7–6–5–4–3–2–11234567–7–6–5–4–3–2–11234567OxyT
(a) Rotate trapezium T 180° about the origin. Label A. (1) (b) Translate trapezium T by vector (–1, –3). Label B. (1)
(a) Rotate trapezium **T** 180° about the origin.
Label the new trapezium **A**. [1 mark]
(b) Translate trapezium **T** by the vector (-1-3)
Label the new trapezium **B**. [1 mark]
Worked Solution & Answer
(a)
(x, y) → (–x, –y) B1
Answer (a): Trapezium A at (–2, 1), (–4, 1), (–5, 2), (–2, 2)
(b)
(x, y) → (x – 1, y – 3) B1
Answer (b): Trapezium B at (1, –4), (3, –4), (4, –5), (1, –5)
Question Paper (PDF) • Mark Scheme (PDF)
Question 4 AQA Nov 2023 2F Q19
[3 marks]
–5–4–3–2–112345–5–4–3–2–112345xyOAB
Describe fully the single transformation that maps shape A to shape B.
Worked Solution & Answer
The shape has been rotated by 180° M1
Center of rotation is the midpoint between corresponding vertices, for example (-4, -2) and (5, 2): x = -4 + 52 = 0.5, y = -2 + 22 = 0 M1
Full description: Rotation, 180°, center (0.5, 0). A1
–5–4–3–2–112345–5–4–3–2–112345xyOABCenter (0.5, 0)
Answer: Answer Rotation 180° about (0.5, 0)
Question Paper (PDF) • Mark Scheme (PDF)
Question 5
[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
Question Paper (PDF) • Mark Scheme (PDF)
Question 6 IGCSE Jan 2023 2HR Q2 / 2FR Q16
[3 marks]
–6–5–4–3–2–1123456–6–5–4–3–2–1123456OxyA
(a) Rotate triangle A 180° about (1, –1) and label it B (2) (b) Translate triangle A by vector (-7, 3) and label it C (1).
(a) On the grid, rotate triangle **A** 180° about (1, -1)
Label the new triangle **B** [2 marks]
(b) On the grid, translate triangle **A** by the vector (-73)
Label the new triangle **C** [1 mark]
Worked Solution & Answer
(a)
Rotating (3, 1), (5, 1), (3, 2) by 180° about (1, -1) gives (-1, -3), (-3, -3), (-1, -4) M1 A1
Answer (a): Triangle B with vertices (-1, -3), (-3, -3), (-1, -4)
(b)
Subtracting 7 from x and adding 3 to y gives (-4, 4), (-2, 4), (-4, 5) B1
Answer (b): Triangle C with vertices (-4, 4), (-2, 4), (-4, 5)
Question Paper (PDF) • Mark Scheme (PDF)
Question 7 IGCSE Jan 2023 1F Q14
[4 marks]
(a) Rotate triangle A 90° anticlockwise about O (2) (b) Describe fully the single transformation that maps triangle B onto triangle C (2)
(a) On the grid, rotate triangle A 90° anticlockwise about centre O [2 marks]
xyO–6–5–4–3–2–1123456–6–5–4–3–2–1123456A
(b) Describe fully the single transformation that maps triangle B onto triangle C [2 marks]
xyO–2–112345678910–2–112345678910BC
Worked Solution & Answer
(a)
(x, y) → (−y, x): (2, −1) → (1, 2), (2, −3) → (3, 2), (5, −3) → (3, 5) M1 A1
Answer (a): Triangle with vertices at (1, 2), (3, 2) and (3, 5)
(b)
Lengths multiplied by 3 and rays pass through origin O(0, 0) M1 C1
Answer (b): Enlargement, scale factor 3, centre (0, 0)
Question Paper (PDF) • Mark Scheme (PDF)
Question 8 IGCSE Jun 2022 2F Q14
[4 marks]
yxO–6–5–4–3–2–1123456–6–5–4–3–2–1123456AB
(a) Describe fully the single transformation that maps shape A onto shape B. (2) (b) On the grid, reflect shape A in the line x = –1. (2)
(a) Describe fully the single transformation that maps shape **A** onto shape **B**. [2 marks]
(b) On the grid, reflect shape **A** in the line with equation x = -1 [2 marks]
Worked Solution & Answer
(a)
Every vertex (x, y) maps to (–x, –y) → rotation 180° about the origin M1 C1
Answer (a): Rotation 180° about (0, 0) (or enlargement scale factor –1, centre (0, 0))
(b)
Shape reflected in x = –1 with vertices (–4, 1), (–6, 1), (–6, 3), (–5, 3), (–5, 4), (–4, 4) M1 A1
Answer (b): Shape reflected in x = –1 with vertices (–4, 1), (–6, 1), (–6, 3), (–5, 3), (–5, 4), (–4, 4)
Question Paper (PDF) • Mark Scheme (PDF)
Question 9 IGCSE Jun 2024 2F Q14
[4 marks]
Oxy–6–6–5–5–4–4–3–3–2–2–1–1112233445566AB
(a) Describe fully the single transformation that maps shape A onto shape B (2) (b) Reflect shape A in the line y = –1 (2)
(a) Describe fully the single transformation that maps shape **A** onto shape **B** [2 marks]
(b) On the grid, reflect shape **A** in the line with equation y = –1 [2 marks]
Worked Solution & Answer
(a)
Every vertex (x, y) of A maps to (−x, −y) in B M1
⇒ rotation of 180° about (0, 0) C1
Answer (a): Rotation 180° about the origin (0, 0)
(b)
Reflect across y = −1 M1 A1
Answer (b): Reflected trapezium drawn with vertices (2, –3), (5, –3), (5, –4), (2, –5)
Question Paper (PDF) • Mark Scheme (PDF)
Question 10 IGCSE Jun 2023 1F Q19 / 1H Q4
[8 marks]
The diagram shows a sketch of triangle **A** and triangle **B** on a coordinate grid.
xyOA(–7, 2)(–11, –5)(f, –3)B(6, 12)(2, d)(9, e)Diagram NOTaccurately drawn
(a) Given that triangle **A** has been translated to give triangle **B**, work out the value of d, the value of e and the value of f [3 marks]
(b) Describe fully the single transformation that maps shape **P** onto shape **Q** [3 marks]
112233445566778899101011111212OxyPQ
(c) On the grid above, rotate shape **P** 90° clockwise about (3, 5)
Label your shape **R** [2 marks]
Worked Solution & Answer
(a)
Translation vector = (6 – –7, 12 – 2) = (13, 10). d = –5 + 10 = 5, e = –3 + 10 = 7, f = 9 – 13 = –4 M2 A1
Answer (a): d = 5, e = 7, f = –4
(b)
Enlargement, scale factor 3, centre (0, 2) M2 C1
Answer (b): Enlargement, scale factor 3, centre (0, 2)
(c)
Shape R drawn at vertices (0, 5), (1, 5), (1, 6), (3, 6) M1 A1
Answer (c): Shape R drawn at vertices (0, 5), (1, 5), (1, 6), (3, 6)
Question Paper (PDF) • Mark Scheme (PDF)
Score: 0 / 10 (0 / 34 marks)
Rotations Worksheets Next: Reflections →

Grade 3 Quizzes

24 Topics
3A - Error intervals3B - Operations with fractions
3C - Estimation3D - Writing and simplifying ratio
3E - Ratio3F - Proportion recipes
3G - Percentages3H - Percentage change
3J - Exchange rates3K - Conversions and units
3L - Scale drawings3M - Best buy questions
3N - Substitution3P - Solving linear equations
3Q - Straight line graphs3R - Area and circumference
3S - Rotations3T - Reflections
3U - Enlargements3V - Translations
3W - Mixed transformations3X - Area of compound shapes
3Y - Frequency trees3Z - Two way tables