The four transformations: translation by a vector, reflection in a line, rotation about a point, and enlargement by a scale factor including fractional and negative scale factors (Higher tier), and describing a single transformation fully.

What this dot point is asking

Edexcel expects you to carry out and fully describe the four transformations: translation, reflection, rotation and enlargement, including fractional and negative scale factors at Higher tier. A common high-value skill is describing a single transformation completely, because each type needs specific information, and a partial description loses marks.

Translation

A translation moves every point of a shape the same distance in the same direction, with no turning or resizing.

So the vector $\begin{pmatrix} 3 \\ -2 \end{pmatrix}$ moves a shape $3$ right and $2$ down. To describe a translation fully, you only need to state "translation" and the vector.

Reflection

A reflection flips a shape across a mirror line so that the image is the same distance behind the line as the object is in front. To describe a reflection fully, name the mirror line by its equation, such as the x-axis ($y = 0$), the y-axis ($x = 0$), or a diagonal like $y = x$ or $y = -x$. Each point and its image are equidistant from the line, on a perpendicular to it.

Rotation

A rotation turns a shape about a fixed point (the centre of rotation) through a given angle and direction. To describe a rotation fully you need three pieces of information: that it is a rotation, the angle and direction (for example $90^\circ$ clockwise), and the centre. Tracing paper is the practical tool: place it over the shape, pin the centre, and turn. The shape keeps its size, so a rotation is never an enlargement.

Enlargement

An enlargement changes a shape's size by a scale factor, measured from a centre of enlargement.

To describe an enlargement fully, state "enlargement", the scale factor, and the centre of enlargement.

Finding the centre of an enlargement

A common reverse question gives an object and its enlarged image and asks for the centre and scale factor. To find the scale factor, divide an image length by the matching object length. To find the centre, draw straight lines (rays) through pairs of corresponding points (each object vertex to its image vertex) and extend them; the centre of enlargement is where all the rays meet. This works for positive and negative scale factors, although with a negative factor the rays cross the centre and continue to the opposite side. Reading the scale factor's sign from whether the image is on the same side (positive) or opposite side (negative) of the centre is a useful check.

Try this

Q1. A shape is translated by the vector $\begin{pmatrix} -2 \\ 5 \end{pmatrix}$. Describe the movement in words. [1 mark]

• Cue. $2$ units left and $5$ units up.

Q2. A triangle is enlarged by scale factor $3$. Its original area is $4\,\text{cm}^2$. What is the area of the image? [2 marks]

• Cue. Area scales by $3^2 = 9$, so the image area is $4 \times 9 = 36\,\text{cm}^2$.