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Mixed transformations Quiz

Grade 3 • 3W • 10 Questions (37 Marks)

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

Explanation:

When a question asks for the single transformation that maps shape A onto shape B, you must name only one of the four transformations: Translation (with column vector), Reflection (with mirror line equation), Rotation (with angle, direction, and centre), or Enlargement (with scale factor and centre).

Never combine two transformations in your description (e.g. “reflected and then translated” scores 0 marks). Check the size first (changed size = Enlargement), then orientation (same way up = Translation; flipped = Reflection; turned = Rotation).

Example 1: Triangle A is reflected in the x-axis to B, then in the y-axis to C. Describe the single transformation from A to C.

A B C
(2,3) → (2,−3) → (−2,−3).
Half-turn around origin:
Rotation, 180°, about (0, 0)

Example 2: Shape P is translated by 3
−2 then −1
6 to Q. Describe the single transformation.

P Q
Add vectors:
3 + (−1) = 2;  −2 + 6 = 4
Translation 2
4
Question 1
[1 mark]
Point A(3, 3) is reflected in the line y = x.
Write down the coordinates of the image point.
Worked Solution & Answer
Reflection in y = x swaps the coordinates: (3, 3) → (3, 3). B1
Answer: (3, 3)
Question 2
[1 mark]
Point A(3, 1) is reflected in the line y = x.
Write down the coordinates of the image point.
Worked Solution & Answer
Reflection in y = x swaps the coordinates: (3, 1) → (1, 3). B1
Answer: (1, 3)
Question 3 AQA Nov 2018 3F Q15
[3 marks]
xyO–4–22442–2–4AB
Describe fully the single transformation that maps shape A to shape B.
Describe fully the single transformation that maps shape A to shape B.
Worked Solution & Answer
The orientation of the shape is reversed, so it is a reflection M1
Connecting corresponding vertices: midpoint of (-4, 4) and (-4, -4) is (-4, 0) M1
midpoint of (-4, 1) and (-1, -4) is (-2.5, -1.5)
The line through these midpoints has gradient -1 and equation y = -x - 4. C1
xyO–4–22442–2–4ABy = -x - 4
Answer: Transformation Reflection in the line y = -x - 4
Question Paper (PDF) • Mark Scheme (PDF)
Question 4 Practice Set 3 2H Q12
[3 marks]
xyAB–2–112345678910–2–112345678910O
Describe fully the single transformation that maps triangle A onto triangle B.
Describe fully the single transformation that maps triangle A onto triangle B.
Worked Solution & Answer
Rotation of 90° clockwise about (1, 4) M2 C1
Answer: Rotation, 90° clockwise, centre (1, 4)
Question Paper (PDF) • Mark Scheme (PDF)
Question 5 Eduqas Nov 2023 2F Q18
[4 marks]
The grid below shows triangle A and triangle B.
–6–5–4–3–2–1123456–4–3–2–112345678xyAB
(a) Describe fully the single transformation that maps triangle A onto triangle B. [2 marks]
(b) Translate triangle A using the vector (-32), label it C. [2 marks]
Worked Solution & Answer
(a)
Triangle A is rotated 90° clockwise M1
Perpendicular bisectors of corresponding vertices intersect at (0.5, -0.5). C1
Answer (a): Rotation of 90° clockwise about center (0.5, -0.5) (or 270° anticlockwise)
(b)
(2,1)+(-3,2)=(-1,3) M1
(6,1)+(-3,2)=(3,3)
(5,4)+(-3,2)=(2,6). A1
Answer (b): Triangle C drawn with vertices (-1, 3), (3, 3), (2, 6)
Question Paper (PDF) • Mark Scheme (PDF)
Question 6 Practice Set 4 1H Q10
[4 marks]
Work out
(a) Describe fully the single transformation that maps triangle P onto triangle Q. (2)
(b) Enlarge rectangle R, with scale factor 3 and centre (4, 0). (2)
(a) Describe fully the single transformation that maps triangle P onto triangle Q. [2 marks]
xyPQ–2–112345678910–2–11234567O
(b) Enlarge rectangle R, with scale factor 3 and centre (4, 0). [2 marks]
xyR–2–112345678910–2–11234567O
Worked Solution & Answer
(a)
Reflection in x = 5 M1 C1
Answer (a): Reflection in the line x = 5
(b)
Scale factor 3 from (4, 0): vertices (1, 3), (7, 3), (7, 6), (1, 6) M1 A1
xyRR'–2–112345678910–2–11234567O
Answer (b): Enlarged rectangle drawn with vertices at (1, 3), (7, 3), (7, 6), (1, 6)
Question Paper (PDF) • Mark Scheme (PDF)
Question 7 IGCSE Jan 2022 1FR Q12
[4 marks]
–7–6–5–4–3–2–1123456789–2–1123456789OxyAB
Work out
(a) Describe fully the single transformation that maps triangle A onto triangle B. (b) Enlarge triangle A with scale factor 2 and centre O, label it C.
(a) Describe fully the single transformation that maps triangle A onto triangle B [2 marks]
(b) On the grid above, enlarge triangle A with scale factor 2 and centre O
Label your triangle C [2 marks]
Worked Solution & Answer
(a)
Midline between x = 2 and x = –4 is x = –1 M1 C1
Answer (a): Reflection in the line x = –1
(b)
Multiply coordinates (2,1), (4,1), (2,4) by 2 → (4,2), (8,2), (4,8) M1 A1
Answer (b): Triangle C drawn with vertices at (4, 2), (8, 2) and (4, 8)
Question Paper (PDF) • Mark Scheme (PDF)
Question 8 IGCSE Nov 2020 1F Q13
[5 marks]
(a) Reflect shaded triangle in y = 2 (2) (b) Describe single transformation mapping triangle A onto triangle B (3)
(a) On the grid, reflect the shaded triangle in the line with equation y = 2 [2 marks]
yx−4−3−2−1123456−5−4−3−2−1123456789O
(b) Describe fully the single transformation that maps triangle **A** onto triangle **B**. [3 marks]
yx−2−11234567−7−6−5−4−3−2−112345OAB
Worked Solution & Answer
(a)
Reflect across y = 2 gives (3, 5), (5, 5), (5, 8) M1 A1
Answer (a): Triangle with vertices at (3, 5), (5, 5) and (5, 8)
(b)
Rotation, 90° anticlockwise (or 270° clockwise), centre (0, 0) M2 C1
Answer (b): Rotation of 90° anticlockwise about (0, 0)
Question Paper (PDF) • Mark Scheme (PDF)
Question 9 IGCSE Jan 2021 2HR Q5 / 2FR Q16
[6 marks]
Here is a shape **P** drawn on a grid of squares.
–10–8–6–4–22468101214–8–6–4–2246810OP
(a) On the grid, rotate shape **P** 180° about the point (-3, 2).
Label the new shape **Q**. [2 marks]
(b) On the grid, translate shape **P** by the vector (108).
Label the new shape **R**. [1 mark]
(c) Describe fully the single transformation that maps triangle **T** onto triangle **U**. [3 marks]
–4–3–2–1O1234567891011121234567TU
Worked Solution & Answer
(a)
Rotate each vertex 180° about (–3, 2) M1 A1
Answer (a): Shape Q with vertices (–6, 6), (–9, 6), (–9, 9), (–3, 9)
(b)
Add (10, 8) to each vertex of P B1
Answer (b): Shape R with vertices (10, 6), (13, 6), (13, 3), (7, 3)
(c)
Base increases from 3 to 6 ⇒ scale factor 2 M2
rays through corresponding vertices meet at (–3, 3) C1
Answer (c): Enlargement, scale factor 2, centre (–3, 3)
Question Paper (PDF) • Mark Scheme (PDF)
Question 10 IGCSE Jan 2019 1F Q16 / 1H Q2
[6 marks]
yx−4−22468O246810AB
Work out
(a) Describe transformation from A to B (3) (b) Translate A by (2, -5) to C (1) (c) Enlarge D with scale factor 1/2 and centre (-4, 2) (2)
(a) Describe fully the single transformation that maps triangle **A** onto triangle **B**. [3 marks]
(b) On the grid, translate triangle **A** by the vector (2-5)
Label the new triangle **C**. [1 mark]
(c) On the grid, enlarge triangle **D** with scale factor 12 and centre (-4, 2) [2 marks]
yx−4−22468O−22468D
Worked Solution & Answer
(a)
Rotation 90° clockwise about (−2, 3) M2 C1
Answer (a): Rotation, 90° clockwise, centre (−2, 3)
(b)
(−2, 2), (−2, 4), (−1, 4) B1
Answer (b): Triangle C at (−2, 2), (−2, 4), (−1, 4)
(c)
(−2, 1), (−2, 3), (−1, 3) M1 A1
Answer (c): Triangle at (−2, 1), (−2, 3), (−1, 3)
Question Paper (PDF) • Mark Scheme (PDF)
Score: 0 / 10 (0 / 37 marks)
Mixed transformations Worksheets Next: Area of compound shapes →

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