# decision trees and numeric attributes

I have been reading a book about Decision Trees and it caught my attention the following part:

In case of numeric attributes, decision trees can be geometrically interpreted as a collection of hyperplanes, each orthogonal to one of the axes

I tried to look for information about this in Internet, but I did not find anything. To what the author refers in this point?

Each vertex in a decision tree is associated with a question of the form "$$x_i < c$$?" (or "$$x_i \leq c$$?"), where $$x_i$$ is one of the input and $$c$$ is a constant. The decision whether to go left or right then depends on which side of the hyperplane $$x_i = c$$ the input is located.
The possible hyperplanes which come up this way are not arbitrary – they are orthogonal to one of the axes; the hyperplane $$x_i = c$$ is orthogonal to the $$x_i$$ axis. An example of a different hyperplane, which cannot occur, is $$x_1 - x_2 = 0$$.