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Reflections

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

Download free reflections worksheets (PDF), GCSE maths past paper questions and worked solutions for Reflections (3T). 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 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 reflections revision notes and worked examples with diagrams, try real GCSE past paper reflections questions with step-by-step solutions, or download a PDF of all reflections worksheet links.

Free Reflections PDF Worksheets & Answers

Grade 3 • Topic 3T
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PMT (Edxl)
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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 Reflections: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

To describe a reflection fully (2 marks), you must state: (1) the word reflection, and (2) the equation of the mirror line. Know the key mirror lines: the x-axis is y = 0, the y-axis is x = 0, vertical lines are x = k, horizontal lines are y = k, and diagonal lines are y = x or y = −x.

To reflect a shape, draw the mirror line first, then count the perpendicular distance from each vertex to the mirror line and count the exact same distance on the opposite side.

Example 1: Point P(−2, 5) is reflected in the vertical mirror line x = 1. Find the coordinates of P'.

P(−2,5) P'(4,5) 3 3 x = 1
−2 to 1 is 3 right.
3 more right: 1 + 3 = 4.
Answer: (4, 5)

Example 2: Shape A has vertex (1, 4) and its reflected image B has corresponding vertex (4, 1). Describe the transformation.

A(1,4) B(4,1) y = x
Coordinates swap: (1, 4) → (4, 1).
Reflection in the line y = x
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Reflections Questions & Answers

Past Paper Example 1 GCSE Jun 2017 2H Q9 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
The diagram shows triangle **A** drawn on a grid.
–5–4–3–2–112345–5–4–3–2–112345OyxA
Kyle reflects triangle **A** in the x-axis to get triangle **B**.
He then reflects triangle **B** in the line y = x to get triangle **C**.
Amy reflects triangle **A** in the line y = x to get triangle **D**.
She is then going to reflect triangle **D** in the x-axis to get triangle **E**.
Amy says that triangle **E** should be in the same position as triangle **C**.
Is Amy correct?
You must show how you get your answer.
Worked Solution & Mark Scheme (3 marks)
A = (3,3), (4,3), (4,1) M1
Reflect in x-axis -> B = (3,–3), (4,–3), (4,–1)
Reflect B in y = x -> C = (–3,3), (–3,4), (–1,4) (rotation 90° anticlockwise about O) M1
Reflect A in y = x -> D = (3,3), (3,4), (1,4)
Reflect D in x-axis -> E = (3,–3), (3,–4), (1,–4) (rotation 90° clockwise about O)
So Amy is not correct. A1
–5–4–3–2–112345–5–4–3–2–112345OyxABCDENo (C and E are in different positions)
Answer: No; C has vertices (–3, 3), (–3, 4), (–1, 4) whereas E has vertices (3, –3), (3, –4), (1, –4).
Past Paper Example 2 IGCSE Jun 2018 1HR Q3 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
–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 & Mark Scheme (3 marks)
Part (a) Solution:
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)
Part (b) Solution:
Subtract (4, 6) → T(1,–3),(2,–3),(2,–1) B1
Answer (b): Triangle T at (1, –3), (2, –3), (2, –1)
Past Paper Example 3 OCR Nov 2022 6H Q1 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
Shape **A** and shape **B** are drawn on the coordinate grid.
–7–7–6–6–5–5–4–4–3–3–2–2–1–1112233445566770ABxy
(a) Describe fully the single transformation that maps shape **A** onto shape **B**. [2 marks]
(b) Reflect shape **A** in the line x = -1. [2 marks]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
Each vertex of shape A moves 5 units right and 6 units down M1
⇒ Translation by vector (5, −6). C1
Answer (a): Translation by vector (5, −6).
Part (b) Solution:
Reflect each vertex across the vertical line x = −1: (−2, 1) → (0, 1), (−4, 1) → (2, 1), (−4, 4) → (2, 4), (−3, 4) → (1, 4), (−3, 2) → (1, 2), (−2, 2) → (0, 2). M1 A1
Answer (b): Reflected L-shape with vertices (0, 1), (2, 1), (2, 4), (1, 4), (1, 2), (0, 2)

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