What is a transformation? And what are the four types of transformations?

In plane geometry a transformation is a process of changing the position of every point on a plane in a way that satisfies certain rules.

Transformations are usually symmetric in a sense that, if there is a transformation that transforms point `A` to point `B`, there is another transformation of the same type that transforms `B` to `A`.

For instance, translation (shift) by `5` of all points on a plane in certain direction has a symmetrical counterpart - shift by `5` in the opposite direction.
Reflection relative to a straight line is a counterpart to itself since the same reflection repeated again transforms a point back to its original position.

Transformations are usually transitive in a sense that, if one particular type of transformation of some type transforms point `A` to point `B` and another one of the same type transforms point `B` to point `C`, there is a transformation of the same type that combines the first two transformations and transforms point `A` into point `C`.

For instance, rotation of all points on a plane around some fixed point counterclockwise by `90^o` and another one, rotating around the same point by `30^o` clockwise can be combined into one rotation - rotation by `60^o` counterclockwise around the same point.

In every type of transformation we have the one that does nothing. For example, scaling by a factor of `1`, translation (shift) by a distance `0` or rotation- by an angle `0^o`. This property of transformations is called _reflexivity.