Learning pack · IGCSE handout

Transformations

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). The four plane transformations are translation, reflection, rotation and enlargement. Describe each with the full set of required details.

Resources at the top · full summary · videos with short notes below.

🎒 Resources in this pack

Jump straight to the printable files, or scroll to the summary and videos.

Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 🎬 More topic videos (6)📖 Full summary

Files: 14_transformations_handout.pdf · 14_transformations_handout_answers.pdf

Full topic summary

The four plane transformations are translation, reflection, rotation and enlargement. Describe each with the full set of required details.

Key learning points

Translation → column vector; reflection → mirror line; rotation → centre, angle, direction; enlargement → centre and scale factor.
Scale factor $>1$ enlarges; $0<k<1$ reduces; negative $k$ rotates $180^\circ$ as well.
Invariant points stay fixed (e.g. points on a mirror line).

Worked example 1 — Translation

Translate $(1,2)$ by $\begin{pmatrix}3\\-1\end{pmatrix}$ .

Working

(4,1)

Add components.

Worked example 2 — Enlargement

Centre O, SF $2$ , point $(3,1)$ . Image?

Working

(6,2)

Multiply coordinates by SF.

Worked example 3 — Reflection

Reflect $(4,-2)$ in the $x$ -axis.

Working

(4,2)

Negate $y$ .

Worked example 4 — Enlargement scale factor

Image lengths are 3 times object lengths from centre O. Scale factor?

Working

k=3

Also state the centre of enlargement in a full description.

🎬 Topic videos

Cross products in the light of linear transformations | Chapter 11, Essence of linear algebra
3Blue1Brown · 13 min
Classroom-ready explain of transformations. Use when teaching this topic in Lower Secondary / IGCSE.
Linear transformations and matrices | Chapter 3, Essence of linear algebra
3Blue1Brown · 11 min
Classroom-ready explain of transformations. Use when teaching this topic in Lower Secondary / IGCSE.
Nonsquare matrices as transformations between dimensions | Chapter 8, Essence of linear algebra
3Blue1Brown · 4 min
Classroom-ready explain of transformations. Use when teaching this topic in Lower Secondary / IGCSE.
Three-dimensional linear transformations | Chapter 5, Essence of linear algebra
3Blue1Brown · 5 min
Classroom-ready explain of transformations. Use when teaching this topic in Lower Secondary / IGCSE.
Why Laplace transforms are so useful
3Blue1Brown · 23 min
Classroom-ready explain of transformations. Use when teaching this topic in Lower Secondary / IGCSE.
Trigonometry and Reflecting Lasers (Ultimate Classroom lesson)
Eddie Woo · 5 min
Classroom-ready explain of transformations. Use when teaching this topic in Lower Secondary / IGCSE.

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