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Translations

Free Printable Translations PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 3)

Download free translations worksheets (PDF), GCSE maths past paper questions and worked solutions for Translations (3V). This is a Grade 3 geometry topic from the GCSE questions by topic collection for Foundation and 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 IGCSE MT, Maths Genie, Corbett Maths, Dr Austin, 1st Class Maths, Maths4EveryOne, E Classroom and PMT, along with past paper question booklets.

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

Free Translations PDF Worksheets & Answers

Grade 3 • Topic 3V
Resource Questions Answers
GCSE past paper questions & solutions
 Qs Ans
IGCSE (9–1) past paper booklet
 Qs Ans
Graded exam questions & solutions
 Qs Ans
Practice Questions & answers
 Qs Ans
Textbook Exercise & answers
 Qs Ans
Practice grid / worksheet & answers
 Qs Ans
Practice grid / worksheet & answers
 Qs Ans
Edexcel exam questions & solutions
 Qs Ans
AQA exam questions & solutions
 Qs Ans
KS2 SATs questions & solutions
 Qs Ans
GCSE topic booklet & answers
 Qs Ans
PMT (Edxl)
Edexcel GCSE topic questions & solutions
 Qs Ans
PMT (AQA)
AQA GCSE topic questions & solutions
 Qs Ans
PMT (IGCSE)
Edexcel IGCSE topic questions & solutions
 Qs Ans
Interactive online lesson & practice
 Page
Grade 3 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
GCSE Maths Grade 3 Revision Notes & Method

Guide to Translations: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

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
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Translations Questions & Answers

Past Paper Example 1 IGCSE Jun 2019 1FR Q14 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
(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 & Mark Scheme (4 marks)
Part (a) Solution:
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)
Part (b) Solution:
Rotation (), 90° clockwise / 270° anticlockwise (), centre (0, 0) or O () M2 C1
Answer (b): Rotation 90° clockwise about (0, 0)
Past Paper Example 2 Eduqas Nov 2021 2H Q5 6 marks
Full Paper (PDF) • Mark Scheme (PDF)
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]
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 & Mark Scheme (6 marks)
Part (a) Solution:
p + 2q = (3-5) + 2(1.52) = (3 + 3-5 + 4) = (6-1) M1 A1
Answer (a): (6-1)
Part Solution:
Translate each vertex of A 6 units right and 1 unit down. M1 A1
Answer : Shape B correctly drawn with vertices (2, 1), (4, 1), (4, 2), (3, 2), (3, 4), (2, 4).
Part (b) Solution:
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
Past Paper Example 3 Eduqas Nov 2021 2F Q22 6 marks
Full Paper (PDF) • Mark Scheme (PDF)
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]
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 & Mark Scheme (6 marks)
Part (a) Solution:
p + 2q = (3, -5) + 2(1.5, 2) = (3 + 3, -5 + 4) = (6, -1). M1 A1
Answer (a): (6-1)
Part Solution:
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 : Shape B drawn with vertices translated by (+6, -1)
Part (b) Solution:
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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