The Four Transformations

Understanding the Four Transformations

  • In the world of mathematics, transformations refer to the processes that alter the size, shape, or position of a figure.
  • The four types of transformations are translation, reflection, rotation, and enlargement.

Translation

  • Translation involves moving a shape to a new position without changing its size or orientation.
  • A shape can be translated any distance in any direction. The distance and direction for translation is often described as a vector.
  • In 2D, a vector [a, b] shows that the shape moves a units to the right and b units up.

Reflection

  • Reflection flips a shape over a mirror line, creating a mirror image of the shape on the opposite side of the line.
  • The original shape and its reflection are identical in size and shape, but opposite in orientation.
  • The reflected shape stays the same distance from the mirror line as the original shape.

Rotation

  • Rotation turns a shape around a fixed point known as the centre of rotation.
  • A rotation is described by the angle of rotation, the centre of rotation, and the direction of rotation (clockwise or anticlockwise).
  • The original shape and the rotated shape are identical in size and shape.

Enlargement

  • Enlargement changes the size of a shape but keeps its shape unchanged. It can make the shape larger or smaller.
  • An enlargement is described by a centre of enlargement and a scale factor.
  • If the scale factor is greater than 1, the shape becomes larger; if it’s less than 1 but greater than 0, the shape shrinks.
  • The shape and its enlargement remain similar, meaning their corresponding angles are equal and their corresponding sides are in proportion.

Summing up the Four Transformations

Transformations are fundamental to understand because they help us understand how shapes can be manipulated and still retain their basic identity. The theory of transformations lies at the core of many phenomena in the natural world and is a key concept in fields as diverse as physics and computer animation. Practice applying these four transformations to various shapes to become familiar with their effects.