A transformation moves, turns, flips, or resizes a shape on a grid. The starting shape is the object; the result is the image.

• Translations, reflections and rotations keep the size and shape identical — the image is congruent to the object.
• Enlargements keep the shape but change the size — the image is similar to the object.

Core tier note: rotations only use multiples of $90°$, reflections are only in a vertical or horizontal line, and enlargement scale factors are positive or fractional (never negative). Only single transformations are examined — never combinations.

The equation of the mirror line, e.g. $x = 2$ or $y = -1$. Just saying "it's a reflection" is not enough — the exact line must be given.

Three things, always: the angle, the direction (clockwise or anticlockwise), and the centre of rotation.

Example: triangle $P$ has vertices $(1,1)$, $(3,1)$, $(1,4)$. After a transformation, triangle $Q$ has vertices $(-1,1)$, $(-1,3)$, $(-4,1)$. Describe the single transformation mapping $P$ onto $Q$.

1. Side lengths are unchanged, so this is a rotation, reflection, or translation — not an enlargement.
2. The orientation has turned rather than flipped or slid, so test a rotation about the origin.
3. A $90°$ anticlockwise rotation sends $(x,y) \to (-y,x)$. Check $(1,1) \to (-1,1)$ ✓ and $(3,1) \to (-1,3)$ ✓.
4. Answer: rotation of $90°$ anticlockwise about the origin $(0,0)$.

The scale factor and the centre of enlargement.

Example: shape $A$ has vertices $(1,1)$, $(2,1)$, $(1,3)$. Shape $B$ has vertices $(1,1)$, $(3,1)$, $(1,7)$. Describe the transformation mapping $A$ onto $B$.

1. Compare side lengths: the horizontal side grows from $1$ to $2$ units, and the vertical side from $2$ to $6$ units — both scale by factor $2$, so this is an enlargement.
2. The vertex $(1,1)$ stays fixed in both shapes, so it must be the centre of enlargement.
3. Answer: enlargement, scale factor $2$, centre $(1,1)$.

The column vector $\begin{pmatrix} x \\ y \end{pmatrix}$, where the top number is the horizontal shift (positive = right) and the bottom number is the vertical shift (positive = up).

• Describing two transformations instead of one, e.g. "reflected, then moved across". Exam questions always want a single transformation — if your description needs two steps, look again.
• Omitting the centre of a rotation or enlargement, or the direction of a rotation — a partial description loses marks even if the type of transformation is correct.
• Swapping the values in a column vector — the top number is always horizontal movement, the bottom is always vertical.