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Translations Quiz

Grade 3 • 3V • 10 Questions (39 Marks)

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

Explanation:

A translation slides a shape without rotating, reflecting, or resizing it. Translations are written using a column vector x
y, where the top number x is the horizontal movement (+ right, − left) and the bottom number y is the vertical movement (+ up, − down).

When finding the translation vector from shape A to shape B, always pick one matching corner on both shapes (e.g. the top-right corner to the top-right corner) rather than counting the gap between the two shapes.

Example 1: Point A(2, −1) is translated by −5
4. Find A'.

A(2,−1) A'(−3,3) −5 +4
Move 5 left, 4 up:
x = 2 − 5 = −3
y = −1 + 4 = 3 → (−3, 3)

Example 2: Top-left vertex of P is (−3, 5) and top-left of Q is (2, 1). Describe the transformation from P to Q.

P Q +5 −4
−3 to 2: +5 (right)
5 to 1: −4 (down)
Translation 5
−4
Question 1 AQA Nov 2020 1F Q13
[2 marks]
Here is a parallelogram.
The parallelogram is translated 4 squares to the left and 3 squares up.
Draw the translated parallelogram.
Answer
Worked Solution & Answer
Translate each vertex 4 units left and 3 units up. M1 A1
Translated shape
Answer: Answer Parallelogram drawn with vertices translated 4 left and 3 up
Question Paper (PDF) • Mark Scheme (PDF)
Question 2
[2 marks]
xyST–5–4–3–2–112345–5–4–3–2–112345O
Describe fully the single transformation that maps shape S onto shape T.
Describe fully the single transformation that maps shape **S** onto shape **T**.
Worked Solution & Answer
Shape S moves 5 units left and 6 units up → Translation by vector (–5, 6) M1 C1
Answer: Translation by vector (-56)
Question Paper (PDF) • Mark Scheme (PDF)
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 IGCSE Jun 2018 1HR Q3
[3 marks]
–5–4–3–2–112345678910–5–4–3–2–112345678OS
(a) Reflect triangle S in the line y = x, label R (2) (b) Translate triangle S by vector (–4, –6), label T (1)
(a) Reflect triangle **S** in the line y = x
Label the new triangle **R**. [2 marks]
(b) Translate triangle **S** by the vector (-4-6)
Label the new triangle **T**. [1 mark]
Worked Solution & Answer
(a)
Swap (x, y) of S(5,3),(6,3),(6,5) → R(3,5),(3,6),(5,6) M1 A1
Answer (a): Triangle R at (3, 5), (3, 6), (5, 6)
(b)
Subtract (4, 6) → T(1,–3),(2,–3),(2,–1) B1
Answer (b): Triangle T at (1, –3), (2, –3), (2, –1)
Question Paper (PDF) • Mark Scheme (PDF)
Question 5 IGCSE Jun 2019 1FR Q14
[4 marks]
(a) Translate shape P by vector (–5, 2). (1) (b) Describe fully the single transformation that maps shape P onto shape T. (3)
(a) On the grid above, translate shape **P** by the vector (–52) [1 mark]
yx–4–22468–4–2246OP
(b) Describe fully the single transformation that maps shape **P** onto shape **T**. [3 marks]
yx–224–4–224OPT
Worked Solution & Answer
(a)
Shift 5 left, 2 up B1
yx–4–22468–4–2246OP
Answer (a): Shape translated to vertices (–3, 3), (–1, 3), (–1, 6), (–2, 6), (–2, 4), (–3, 4)
(b)
Rotation (), 90° clockwise / 270° anticlockwise (), centre (0, 0) or O () M2 C1
Answer (b): Rotation 90° clockwise about (0, 0)
Question Paper (PDF) • Mark Scheme (PDF)
Question 6 IGCSE Jun 2018 1F Q12
[4 marks]
–6–5–4–3–2–1123456–6–5–4–3–2–1123456OyxAB
(a) Describe fully the transformation from A to B. (2) (b) Translate B by (2, –6) and label C. (1) (c) Describe fully the transformation from C to B. (1)
(a) Describe fully the single transformation that maps triangle **A** onto triangle **B**. [2 marks]
(b) On the grid, translate triangle **B** by the vector (2-6)
Label your triangle **C**. [1 mark]
(c) Describe fully the single transformation that maps triangle **C** onto triangle **B**. [1 mark]
Worked Solution & Answer
(a)
Midline between x = –3 and x = 1 is x = –1 M1 C1
Answer (a): Reflection in the line x = –1
(b)
Triangle C drawn with vertices (3, –1), (3, –5), (5, –5)
Answer (b): Triangle C drawn with vertices (3, –1), (3, –5), (5, –5)
(c)
Inverse of translation (2, –6) is (–2, 6) C1
Answer (c): Translation by the vector (–2, 6)
Question Paper (PDF) • Mark Scheme (PDF)
Question 7 OCR Nov 2020 4H Q12
[5 marks]
Triangle **T** is drawn on a coordinate grid.
T–8–7–6–5–4–3–2–1012345678–8–7–6–5–4–3–2–112345678yx
(a) Translate triangle **T** by vector (-62). [2 marks]
(b) Describe fully the **single** transformation that is equivalent to:
• a reflection in the line y = x, followed by
• a reflection in the x-axis.
You may use the grid above to help you. [3 marks]
Worked Solution & Answer
(a)
(2 − 6, 1 + 2) = (−4, 3) M1
(5 − 6, 1 + 2) = (−1, 3)
(5 − 6, 3 + 2) = (−1, 5). A1
Answer (a): Triangle drawn with vertices at (−4, 3), (−1, 3), (−1, 5)
(b)
Reflecting (x, y) in y = x gives (y, x) M2
reflecting in the x-axis gives (y, −x), which is a rotation of 90° clockwise about the origin (0, 0). C1
Answer (b): Rotation of 90° clockwise about (0, 0).
Question Paper (PDF) • Mark Scheme (PDF)
Question 8 IGCSE Jun 2018 1FR Q17
[5 marks]
–5–4–3–2–112345678910–5–4–3–2–112345678OS
(a) Reflect triangle S in y = x, label R (2) (b) Translate S by (–4, –6), label T (1) (c) Describe single transformation mapping P onto Q (2)
(a) Reflect triangle **S** in the line y = x
Label the new triangle **R**. [2 marks]
(b) Translate triangle **S** by the vector (-4-6)
Label the new triangle **T**. [1 mark]
(c) Describe fully the single transformation that maps triangle **P** onto triangle **Q**. [2 marks]
–2–112345678–22468101214PQ
Worked Solution & Answer
(a)
Swap x and y coordinates of S(5,3),(6,3),(6,5) → R(3,5),(3,6),(5,6) M1 A1
Answer (a): Triangle R at (3, 5), (3, 6), (5, 6)
(b)
Subtract (4,6) → T(1,–3),(2,–3),(2,–1) B1
Answer (b): Triangle T at (1, –3), (2, –3), (2, –1)
(c)
Enlargement SF 3 about origin M1 C1
Answer (c): Enlargement, scale factor 3, centre (0, 0)
Question Paper (PDF) • Mark Scheme (PDF)
Question 9 Eduqas Nov 2021 2H Q5
[6 marks]
The grid shows shape A.
–6–5–4–3–2–1123456–6–5–4–3–2–11234560xyA
p and q are translation vectors with
p = (3-5)   and   q = (1.52).
Shape A is mapped to shape B using p + 2q.
(a) Find the column vector which translates shape A to shape B. [2 marks]
(b) Draw and label shape B on the grid. [2 marks]
(b) Triangle C has vertices with coordinates (4, 3), (6, 5), (6, 0). [2 marks]
–20246810–2246810xyC
After a single transformation, the vertices of triangle C are mapped to (3, 4), (5, 6), (0, 6).
Describe the transformation.
Worked Solution & Answer
(a)
p + 2q = (3-5) + 2(1.52) = (3 + 3-5 + 4) = (6-1) M1 A1
Answer (a): (6-1)
(b)
Translate each vertex of A 6 units right and 1 unit down. M1 A1
Answer (b): Shape B correctly drawn with vertices (2, 1), (4, 1), (4, 2), (3, 2), (3, 4), (2, 4).
(b)
Each coordinate (x, y) maps to (y, x): M1
(4, 3) → (3, 4), (6, 5) → (5, 6), (6, 0) → (0, 6)
This is a reflection in the line y = x. A1
Answer (b): Reflection in the line y = x
Question Paper (PDF) • Mark Scheme (PDF)
Question 10 Eduqas Nov 2021 2F Q22
[6 marks]
xy–6–5–4–3–2–1123456–6–5–4–3–2–11234560A
p and q are translation vectors with
p = (3-5) and q = (1.52).
Shape A is mapped to shape B using p + 2q.
(a) (i) Find the column vector which translates shape A to shape B.
(a) (ii) Draw and label shape B on the grid.
(b) Triangle C has vertices with coordinates (4, 3), (6, 5), (6, 0).
After a single transformation, the vertices of triangle C are mapped to (3, 4), (5, 6), (0, 6).
Describe the transformation.
p and q are translation vectors with
p = (3-5) and q = (1.52).
Shape A is mapped to shape B using p + 2q.
(a) Find the column vector which translates shape A to shape B. [2 marks]
(b) Draw and label shape B on the grid. [2 marks]
(b) Triangle C has vertices with coordinates (4, 3), (6, 5), (6, 0).
After a single transformation, the vertices of triangle C are mapped to (3, 4), (5, 6), (0, 6).
Describe the transformation. [2 marks]
Worked Solution & Answer
(a)
p + 2q = (3, -5) + 2(1.5, 2) = (3 + 3, -5 + 4) = (6, -1). M1 A1
Answer (a): (6-1)
(b)
Vertices of A: (-4, 2), (-2, 2), (-2, 3), (-3, 3), (-3, 5), (-4, 5) M1
Vertices of B: (2, 1), (4, 1), (4, 2), (3, 2), (3, 4), (2, 4). A1
Answer (b): Shape B drawn with vertices translated by (+6, -1)
(b)
Each (x, y) coordinate is swapped to (y, x), which represents reflection in the line y = x. M1 A1
Answer (b): Reflection in the line y = x
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Score: 0 / 10 (0 / 39 marks)
Translations Worksheets Next: Mixed transformations →

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