Combinations of Transformations Revision Content

A transformation is the process that changes the position or direction of a shape.
Transformations in maths include translation, reflection, rotation, and enlargement.
A combination of transformations refers to when more than one transformation is performed on a point, line or shape.

A translation is a transformation that moves each point of a shape the same distance in the same direction.
It doesn’t change the shape or size, but only its position.
Translations are denoted as vectors, e.g., (5, -3) meaning move 5 units right and 3 units down.

A reflection is a transformation representing a flip of a shape over a line, known as the line of reflection.
Reflection does not alter the size of a shape; it reverses the orientation.
The corresponding points in the original and reflected shape are equal distance from the line of reflection.

A rotation is a transformation that turns a shape about a fixed point, known as the center of rotation.
The amount of rotation is usually specified in degree or radians, and the direction of rotation (clockwise or anticlockwise).
A rotation does not alter the size or shape, just its orientation and position.

An enlargement is a transformation that alters the size of a shape but not its shape.
It’s defined by its scale factor and its center of enlargement.
If the scale factor is larger than 1, the shape increases in size. If it’s smaller than 1, the shape reduces in size.

Combining transformations involves performing more than one transformation on a shape, one after the other.
The transformations can be the same type or different types. For example, you could perform two rotations, or a translation followed by a reflection.
The order of transformations does matter in certain circumstances. For example, a rotation followed by a translation can yield different results than a translation followed by a rotation.
With proper combination of transformations, every point in the plane can move to any other point.
It’s very common in mathematics curriculum to probe understanding of combinations of transformations.

Every transformation has an inverse transformation, which reverses the effect of the original transformation.
For example, the inverse of a translation by vector (a, b) is a translation by vector (-a, -b).
Applying a transformation and then its inverse brings the shape back to its original position.