# What is the name for this operation?

What is the name for this operation?

Effectively, take a range and adjust its center point to 0 on a number line.

In the case of the example above, I'm specifically looking for the name or operation which takes a number range of -28 to +72, and adjusts it back to -50 to +50.

I should also say, I'm looking for the terminology that hopefully doesn't require a math background. If the official terminology of the process is a pretty technical word, than I would love to see a simpler explanation that would suffice. Something a freshman in highschool would understand. Or even a middle schooler.

• It would be natural to call it a translation of $[-28,72]$. – Git Gud Dec 7 '15 at 23:48
• Added some clarity, I'm hoping for a very simple term. Thanks for the answers thus far though, they all got a +1. Waiting to see if something simpler comes up for the actual answer flag. – Eddie Dec 7 '15 at 23:51
• I've heard it called zero-centering, which is fairly self-explanatory. – Brian Tung Dec 7 '15 at 23:52

To make it understandable to a middle-schooler, you might say that you slide (or move) the whole interval so that its mid-point slides (or moves) to zero.

As have already been mentioned, the technical term is translation, which children might associate with translating between languages. They are absolutely right to make the association, since a word in one language is coupled to a word in another language, just as a point in the interval [-28,72] is coupled to a point in the interval [-50,50].

• "shift" is also a common synonym for geometric translation. – Blue Dec 8 '15 at 0:12

Translation. For example, if you want the point $t_0$ to be $0$ in your new coordinates, make $x=t-t_0$. In your case you are translating by 22, $x=t-22$. Then, $-28\rightarrow -50$ and $72\rightarrow 50$. So your new range is $[-50,50]$ with $22\rightarrow 0$.

In the most general case (interval of any length) there are two operations involved. The first one is a translation that transforms the original interval in one centered in 0 and the second one is an homothetic transformation (just a scaling operation) which reescales everything.

• Would translating and scaling suffice for middle school terminology? More generally it is a mapping. – SteveO Dec 7 '15 at 23:52
• @SteveO Yes, much easier to understand than homothetic transformation. Thank you – A. A. Dec 7 '15 at 23:53

As you are looking for a "very simple terminology" either standardizing or normalizing would be appropriate (changing the z to s may be needed if you are on the other side of the Atlantic). This conforms to the conventions ins many similar situations: Grade Point averages are in the range 0 to 10 in some counties and 0 to 5 in another. Standardization is a process that makes them comparable.