Transformations
Summary: Transformations change the position or orientation of shapes on a coordinate grid. The four types are translation, reflection, rotation, and enlargement, with symmetry describing the natural repetition within a shape. Tags: concepts math y7 geometry transformations Created: 2026-05-30 Last Updated: 2026-05-30
Content
A transformation changes a shape’s position, orientation, or size. The original shape is called the object and the transformed shape is called the image.
Translation
A translation slides every point of a shape the same distance in the same direction. The shape does not rotate, reflect, or change size — it simply moves.
A translation is described using a column vector:
| Vector | Meaning |
|---|---|
| (3, 2) | Move 3 units right, 2 units up |
| (−4, 1) | Move 4 units left, 1 unit up |
| (0, −5) | Move 5 units down (no horizontal change) |
Reflection
A reflection flips a shape over a mirror line. Every point on the shape is the same perpendicular distance from the mirror line as its image, but on the opposite side.
Common mirror lines:
- x-axis (y = 0): (x, y) → (x, −y)
- y-axis (x = 0): (x, y) → (−x, y)
- y = x: (x, y) → (y, x)
- y = −x: (x, y) → (−y, −x)
To describe a reflection fully, state the equation of the mirror line.
Rotation
A rotation turns a shape around a fixed point called the centre of rotation. To describe a rotation fully, you need three things:
- Centre of rotation (the fixed point)
- Angle of rotation (90°, 180°, 270°)
- Direction (clockwise or anticlockwise)
Rotation 180° about the origin maps (x, y) → (−x, −y) regardless of direction.
Symmetry
Line symmetry: A shape has line symmetry if it can be folded along a line so both halves match exactly. An equilateral triangle has 3 lines of symmetry, a square has 4, a rectangle has 2, and a parallelogram has 0.
Rotational symmetry: A shape has rotational symmetry if it looks the same after being rotated through less than 360° about its centre. The order is the number of times the shape matches itself during a full rotation. A square has order 4, an equilateral triangle has order 3, a rectangle has order 2.
Describing Transformations
When describing a transformation fully, include:
- Translation: State it is a translation, give the column vector
- Reflection: State the mirror line equation
- Rotation: State the centre, angle, and direction
Combined Transformations
When multiple transformations are applied, apply them one after the other in the order given. The image of the first transformation becomes the object for the second.