Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed

Transformations

In one sentence. Translation, reflection, rotation and enlargement — performing each, and describing them COMPLETELY, because a partial description scores nothing.

Vectors & Transformations — one of 2 modules in this strand, and one of 53 in Pearson Edexcel International GCSE Mathematics. Both tiers.

This module ends with Felix Klein. Learn Transformations, teach it, then defend it against Felix Klein.

Where this sits in the specification

Specification 4MA1, 5.2 Transformation geometry. Incandio is aligned to this specification; it is not published by, endorsed by or affiliated with Pearson, and the sub-topic numbers are given so you can check every module against your own copy.

  • 5.2 — Transformation geometry

1 · Understand it

What it is

Four ways to move a shape: translation (slide by a column vector), reflection (mirror in a stated line), rotation (turn by an angle, in a direction, about a centre) and enlargement (scale by a factor from a centre — which can be fractional or negative). Describing one FULLY means giving every ingredient: vector; mirror line; angle + direction + centre; scale factor + centre.

Why it works

The description rules exist because each missing ingredient leaves infinitely many candidate transformations — a rotation without its centre could be any of them. Negative enlargement makes sense once you see the rays: points project THROUGH the centre to the other side, so the image flips as well as scales.

When a question is asking for it

'Describe fully the single transformation…' (name it, then list all its ingredients — and note 'single': answering with two combined transformations scores zero), and 'draw the image of…' questions. Combined transformations: apply one at a time, in the stated order.

How to hold it in your head

Memorise each transformation's ingredient list like a recipe card: translation = vector. Reflection = mirror line's equation. Rotation = angle, direction, centre. Enlargement = factor, centre. When describing, write the name, then tick off every ingredient on the card.

2 · The mistakes that cost marks

  • Describing a rotation without the centre (or direction). All three ingredients or no marks.
  • Reflection 'in the x-axis' vs 'in the y-axis' swapped: x-axis flips the y-coordinate, y-axis flips the x.
  • In the vector, mixing the order: top number is the x-move (right/left), bottom is the y-move (up/down).
  • Negative scale factors treated as impossible. SF −2 doubles AND flips through the centre.

3 · Worked examples

Laid out the way an examiner wants working shown — every step is a mark.

Triangle A has vertices (1, 1), (3, 1) and (1, 2). Triangle B has vertices (−1, 1), (−1, 3) and (−2, 1). Describe fully the single transformation that maps A onto B.

  1. Same size and shape, and B is not a mirror image of A (the vertices run round in the same order), so it is a rotation.
  2. Angle and direction: A's horizontal side, (1, 1) to (3, 1), points right; its image, (−1, 1) to (−1, 3), points up. Right → up is a quarter turn anticlockwise.
  3. Centre: test the origin with the rule for 90° anticlockwise, (x, y) → (−y, x): (1, 1) → (−1, 1), (3, 1) → (−1, 3), (1, 2) → (−2, 1). All three match, so the centre is (0, 0). (Off the axes, find the centre with tracing paper, or where the perpendicular bisectors of the lines joining two points to their images meet.)
  4. Write the name, then every ingredient on the card.

Answer: Rotation, 90° anticlockwise, centre (0, 0)

The point P(7, 5) is enlarged by scale factor ½, centre C(1, 3). Find the image of P.

  1. An enlargement scales the journey FROM THE CENTRE: CP = (7 − 1, 5 − 3) = (6, 2).
  2. Scale factor ½: the image is half as far along the same ray, (3, 1) from C.
  3. Image = (1 + 3, 3 + 1) = (4, 4).
  4. (A fractional factor between 0 and 1 makes the image smaller and nearer the centre. To FIND a centre, join each point to its image and extend the lines: they meet at the centre.)

Answer: (4, 4)

4 · Prove it — the five questions

The five questions climb Grade 6 → 9+ and are marked inside Incandio on your own device, against authored accepted forms, with a diagnosis of the wrong answer you actually gave. The answers stay in the app so that the practice is worth doing; the questions themselves are here.

  1. Grade 6 — The point P(3, −2) is translated by the vector (−5, 4) — that is, −5 across and 4 up. Work out the coordinates of the image. (Type it like (-2,2).)
  2. Grade 7 — The point (4, −1) is reflected in the line y = x. Work out the coordinates of the image. (Type it like (-1,4).)
  3. Grade 8 — The point (2, 5) is rotated 90° clockwise about the origin. Work out the coordinates of the image. (Type it like (5,-2).)
  4. Grade 9 — The point (3, −1) is enlarged by scale factor −2, centre the origin. Work out the coordinates of the image. (Type it like (-6,2).)
  5. 9+ — The point (5, 2) is first reflected in the x-axis, and the image is then rotated 180° about the origin. Work out the coordinates of the final image. (Type it like (-5,2).)

Think you understand it?

Reading is the start. On Incandio a topic counts as mastered only once you have taught it and defended it — the two things a revision guide cannot ask of you.

Incandio this topic → Prove it. Teach it. Defend it. What does “Incandio it” mean?

  1. Prove it — five questions on Transformations, marked on the spot, that tell you what was missing rather than just what was wrong.
  2. Teach it — Explain how Transformations works — and why — to Ember, an AI pupil who does not have it yet. The method matters more than the vocabulary.
  3. Defend it — Argue Transformations against Felix Klein — three rounds, marked against descriptors you can read before you begin.
  4. Then the exam — read all 9 authored exam-style questions on this unit, each with its command word and its tariff, then have them marked on Incandio with the mistake you actually made named.

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