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

Dec 10, 2015

The most frequently occurring transformations are translation, rotation, reflection and scaling.

#### Explanation:

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.