Two or more transformations can be combined. If transformation A is followed by transformation B this is written B o A, this reads B follows A.
A reflection in one mirror line followed by a reflection in a parallel mirror line results in a translation of twice the distance between the mirror lines.
e.g. A A ´´ under a reflection in m followed by a reflection in n.
A A ´´ is a translation of
A rotation about a point of x° followed by a second rotation of y° about the same point, results in a rotation of (x + y)° about the point.
An enlargement with scale factor k1, followed by an enlagement with scale factor k2 , gives a combined enlargement with scale factor k1 x k2.
A translation of followed by a translation of gives a combined translation of
i.e. It is a vector addition.