Question

What is a transformation?

Answer 1

An element(point, line, plane or any other geometric, complex or whatever figure) is said to undergo a transformation when ever one or more of its properties are changed.

Explanation:

A transformation just a rule; its more like a function. It takes an object and returns that object's image.

Transformations are done using: functions, matrices, complex numbers etc.

What we call object can be a point, a line etc. The basic fact about all objects is that object haves properties.

For example: The point `A(3,2)` has only the property of position(in a Cartesian coordinate system).

Once you change point `A`'s position to let's say `B(6,4)` by a particular procedure, we say you have transformed point `A` to be point `B`.

And in which case the object is `A(x,y)` and the image is `B(6,4)`

Our transformation could be the matrix: `({:(2" "0),(2" "0):})`

Proof : Because `({:(2" "0),(0" "2):})xx({:(3),(2):})=({:(6),(4):})`