Transformations

Types of Transformation

Translation

A translation slides a shape without rotating or reflecting it. Described by a vector (x, y).

Vector (3, -2): move 3 right, 2 down.

Coordinates: add the vector to each vertex: (1,4) → (4, 2)

Reflection

A reflection flips a shape over a mirror line.

• Reflection in x-axis: (x, y) → (x, -y)
• Reflection in y-axis: (x, y) → (-x, y)
• Reflection in y = x: (x, y) → (y, x)

Rotation

A rotation turns a shape through an angle about a centre of rotation.

Describe with: centre, angle, direction (clockwise or anticlockwise).

Rotation 180° about origin: (x, y) → (-x, -y)

Enlargement

An enlargement changes the size of a shape by a scale factor from a centre of enlargement.

Scale factor 2: all lengths double, all coordinates move further from centre. Scale factor ½: shape shrinks to half size.

Congruence and Similarity

• Translations, reflections, rotations → congruent (same shape and size)
• Enlargements → similar (same shape, different size)