This mini-lesson covers the whole of the Edexcel 4MA1 topic: the four transformations (reflection, rotation, translation, enlargement), how to describe, combine and spot invariant points, then column vectors, their magnitude, arithmetic, and vector geometry proofs.
Work through each screen, answer the questions (some are calculations, some concept checks) and collect ⭐ stars. Screens tagged Higher are Higher-tier only. Press Start.
A transformation maps an object onto an image. The image is often labelled with dashes, e.g. triangle A → triangle A′. Edexcel 4MA1 needs you to carry out and fully describe four transformations:
Key idea: reflection, rotation and translation keep the shape the same size (congruent). Only enlargement changes the size (similar shapes).
A reflection flips a shape across a mirror line. Every point moves to the opposite side of the line, the same distance away. To describe one fully you must give the equation of the mirror line (e.g. x = 0, y = 2, y = x).
Reflect the point (2, 3) in the x-axis (the line y = 0).
The x-coordinate stays; the y-coordinate flips sign: (2, 3) → (2, −3).
A rotation turns a shape about a fixed point. To describe one fully you need three things:
Misconception: saying "rotate 90°" is not enough. Without the centre, the angle and the direction, the description is incomplete and loses marks.
A translation slides a shape without turning or resizing it. It is described by a column vector a
b where the top number is the movement in x (right +) and the bottom number is the movement in y (up +).
Translate (1, 1) by the vector 4
−2.
Add the vector to the point: (1 + 4, 1 + (−2)) = (5, −1).
Misconception: the column vector is top = x, bottom = y — never the other way round. And to reverse a translation you negate both numbers.
An enlargement changes the size of a shape. Describe it with a centre of enlargement and a scale factor (SF). Each point moves so its distance from the centre is multiplied by the SF.
Enlarge the point (2, 1) by scale factor 3, centre the origin.
Multiply each coordinate by the SF: (2 × 3, 1 × 3) = (6, 3).
The scale factor need not be a whole number bigger than 1:
Misconception: a scale factor less than 1 does not mean "no enlargement" — it just makes the image smaller. And a negative SF flips the shape to the other side of the centre; it is not the same as making it smaller.
When asked to describe fully, name the single transformation and give all its details:
You may also do two transformations one after another (a combination). The result can sometimes be described as a single transformation.
Exam tip: if a question says "describe the single transformation", one word (like "reflection") on its own scores nothing — you must add the full details, and never describe it as two transformations.
A point is invariant if it stays exactly where it is after a transformation.
Read each clue and tap the transformation it describes.
Tap a transformation on the left, then its required description on the right.
A vector has both magnitude (length) and direction. We write it as a column vector x
y: top = movement in x, bottom = movement in y. Vectors are printed in bold (a) or underlined (a).
The magnitude (or modulus) is the vector's length. Using Pythagoras on the x- and y-parts:
Find the magnitude of a = 3
4.
|a| = √(3² + 4²) = √(9 + 16) = √25 = 5.
This is a 3–4–5 triangle. A vector and its reverse (e.g. 3
4 and −3
−4) have the same magnitude.
Add or subtract vectors component by component — top with top, bottom with bottom:
Geometrically, a + b means "do a, then b" — placing them nose-to-tail. The single vector from start to finish is the resultant.
Multiplying a vector by a scalar (a number) multiplies both components:
A scalar multiple like 3a is parallel to a (same direction, 3× as long). The vector −a has the same length but points the opposite way.
Misconception: −a is not a shrunk version of a — it is the same length, opposite direction. Only a scalar between −1 and 1 changes the length.
The position vector of a point A is the vector from the origin O to A, written OA (with an arrow above) or a. To go from A to B:
So you always do "finish minus start". This is the key to every vector-geometry proof.
A has position vector 1
2, B has position vector 4
7.
AB = b − a = 4
7 − 1
2 = 3
5.
Exam proofs usually ask you to show two vectors are parallel or that points are collinear (in a straight line). The trick:
Suppose PQ = 2
3 and RS = 4
6.
RS = 2 × 2
3 = 2PQ. Since RS is a scalar multiple of PQ, PQ is parallel to RS (and twice as long).
Reflection: give the mirror line. (a,b)→ across the line.
Rotation: centre + angle + direction.
Translation: column vector x
y (top = x, bottom = y).
Enlargement: centre + scale factor (incl. fractional & negative — Higher).
Invariant points: mirror line / centre of rotation / centre of enlargement.
Magnitude (H): |a| = √(x² + y²).
Arithmetic (H): add/subtract components; scalar × both parts; −a reversed.
Position vectors & proofs (H): AB = b − a; scalar multiple ⇒ parallel.
That's the whole of Edexcel 4MA1 Vectors & Transformation Geometry. Press Finish to see your score.
You've worked through Vectors & Transformation Geometry for Edexcel IGCSE Maths A. 🎉
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