Transformations · GCSE Maths

Reflection and rotation

A reflection is described by its mirror line, such as 'reflection in the y-axis' or 'reflection in the line y = x'.
A rotation is described by its angle, its direction (clockwise or anticlockwise) and its centre, such as 'rotation 90° clockwise about (0, 0)'.
Reflecting (3, 1) in the x-axis gives (3, −1); in the y-axis gives (−3, 1); in the line y = x gives (1, 3).
Rotating (3, 1) about the origin: 90° clockwise gives (1, −3); 180° gives (−3, −1).

A translation slides a shape without turning it. It is described by a column vector: the top number moves it right (positive) or left (negative), and the bottom number moves it up (positive) or down (negative).
A translation 4 right and 2 down moves (1, 5) to (5, 3).

An enlargement is described by its scale factor and its centre of enlargement.
Scale factor 2 doubles every length. Scale factor ½ halves every length, so the shape gets smaller.
To find the centre, draw straight lines through matching corners of the shape and its image. They meet at the centre.
(Higher) With a negative scale factor, the image is on the other side of the centre and upside down.

'Describe fully' needs one transformation with all its details: reflection (mirror line); rotation (angle, direction, centre); translation (vector); enlargement (scale factor, centre).
Reflections, rotations and translations give congruent images. Enlargements give similar images.
(Higher) An invariant point stays in the same place, such as a point on the mirror line of a reflection.

Reflection: Flipping a shape in a mirror line.
Rotation: Turning a shape through an angle about a fixed point.
Translation: Sliding a shape without turning or flipping it.
Enlargement: Changing the size of a shape by a scale factor from a centre.
Scale factor: The number every length is multiplied by in an enlargement.
Centre of enlargement: The fixed point an enlargement is measured from.
Column vector: Two numbers, one above the other, that describe a movement across and up.
Invariant point: A point that does not move under a transformation.