Vectors and Transformations
MYP Mathematics Extended — Geometry & Algebra strand: Vectors and Transformations
This chapter fuses two ideas that examiners love to test together: a vector as a piece of information carrying both size and direction, and a transformation as a rule that moves every point of a shape in a consistent way. The link between them is tighter than it looks — a translation is a vector, an enlargement is a scalar multiplication, and a rotation is a matrix. Once you see that, half the 'new' content in this topic is just arithmetic you already know, applied to coordinates instead of numbers.
Overview
A vector is a quantity with magnitude AND direction — a displacement, a translation, a velocity. Write it as a column , an arrow , or bold . Everything else in this chapter is one of three things: arithmetic on vectors (add, subtract, scale), geometry using vectors (position, displacement, proof), or transformations of shapes — which turn out to BE vector/matrix operations in disguise.
- Vector arithmetic behaves component-by-component — add the top numbers, add the bottom numbers. No cross-multiplying, ever.
- A position vector fixes a point relative to the origin; a displacement vector is the difference between two position vectors — it can start anywhere.
- Four transformations to know cold: translation, reflection, rotation, enlargement. Each needs specific extra information to be 'fully described'.
- Reflections and rotations about the origin can be written as matrices — combining two transformations is then just matrix multiplication, but the order flips.
The shape of the chapter
Command terms that decide your marks here
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| Write down / State | Give the answer directly — no working expected or rewarded. | Knowing | Full marks for correct answer alone; showing extra working wastes time, not marks. |
| Calculate / Find | Obtain a numerical result, normally showing method. | Applying | Method marks awarded even with an arithmetic slip IF the correct process is visible — an answer with zero working can lose method marks. |
| Describe | Give a full account of a transformation: type + ALL defining parameters. | Communicating | A rotation described without centre AND angle AND direction scores zero for that mark, even if the sketch is perfect. |
| Show that | Prove a given statement is true using explicit, connected algebra — the answer is already known, so you must justify every line. | Reasoning | Jumping straight to the given result without intermediate steps earns no credit, even if correct. |
| Justify | Give a valid mathematical reason supporting a conclusion. | Reasoning | A correct final claim with no reasoning attached scores 0 on this command term specifically. |
Key point
Overview