TransformationsCambridge IGCSE Maths: Revision notes

There are four transformations you need to recognise, describe and draw:

• Reflection — flips a shape over a mirror line
• Rotation — turns a shape about a fixed centre by an angle
• Enlargement — resizes a shape by a scale factor from a centre
• Translation — slides a shape without turning or resizing it, using a column vector

For every transformation question, a full description requires stating the type of transformation AND all of its defining details (e.g. the line, centre and angle, or centre and scale factor).

A reflection flips a shape over a mirror line. To fully describe a reflection, state:

• The equation of the mirror line (e.g. $x = 2$, $y = -1$, or $y = x$)

To draw a reflection, each point of the object is mapped to a point the same perpendicular distance from the mirror line, but on the opposite side. Vertical or horizontal mirror lines are tested first; any straight line (including diagonal lines like $y=x$) can appear at Extended level.

A rotation turns a shape about a fixed point. To fully describe a rotation, state:

• The centre of rotation (a coordinate)
• The angle of rotation (e.g. 90°, 180°, 270°)
• The direction (clockwise or anticlockwise) — unless the angle is 180°, where direction does not matter

Rotations can be about the origin, a vertex, or a midpoint of an edge, through multiples of 90°.

An enlargement resizes a shape from a fixed point. To fully describe an enlargement, state:

• The scale factor
• The centre of enlargement (a coordinate)

Scale factors:

• Greater than 1: the image is bigger than the object
• Between 0 and 1 (a fraction): the image is smaller than the object
• Negative (Extended only): the image is on the opposite side of the centre and is inverted

To draw an enlargement, measure the distance from the centre to each vertex and multiply by the scale factor to find the new vertex position.

A translation slides every point of a shape by the same amount, with no rotation, reflection or resizing. To fully describe a translation, state:

• The column vector, e.g. $\binom{3}{-2}$, meaning 3 units right and 2 units down

To draw a translation, move every vertex of the shape by the column vector.

At Extended level, questions may ask you to describe a combination of two transformations applied one after another — describe each transformation fully and in the correct order, as a single equivalent transformation if one exists.