Unit 11 Cambridge IGCSE Maths 0607 Transformations and Vectors

Unit 11 — Quick Summary
Section 1 — Core Transformations
Four types, each described by specific information. A translation slides a shape and is described by a column vector. A reflection flips a shape in a horizontal or vertical mirror line. A rotation turns a shape and needs a centre, an angle (a multiple of ninety degrees), and a direction. An enlargement resizes a shape from a centre by a scale factor; image lengths are the scale factor times the corresponding object lengths.
Section 2 — Extended Transformations
The mirror line for a reflection can now be any straight line, with the lines through the origin at forty-five degrees being especially common. A rotation can be about any centre, found by subtracting the centre, rotating about the origin, and adding the centre back. A negative scale factor inverts the image through the centre of enlargement. To reverse a combination of transformations, reverse each step and apply them in the opposite order.
Section 3 — Vectors
A vector has both magnitude and direction, and can be written as a column, as a directed line-segment between two points, or as a bold lowercase letter. Addition and subtraction are done component by component. The negative of a vector reverses its direction but keeps its magnitude. Multiplying by a scalar stretches the vector and reverses its direction if the scalar is negative. Two non-zero vectors are parallel exactly when one is a scalar multiple of the other.
Section 4 — Magnitude
The magnitude of a vector is its length, found by Pythagoras’ theorem on its two components. The magnitude of the vector from one point to another is simply the distance between those two points. Magnitudes should be given exactly in surd form where possible, otherwise to at least three significant figures.