# Why can we assume WLOG that $x$ is zero?

I am new to mathematics, so I apologize in advance if this question is trivial. I was trying to prove a property of an arbitrary three-point system in $\mathbb{R}^2$ regarding convexity. I tried it without looking at the solution, but to no avail. I looked at the solution and the author assumed WLOG $x$ to be the origin and the proof was really easy.

My question is why can we assume $x$ to be the origin. I think it has something to do with the function $f(a) = x - a$, where $x$ is one of the points in the three-point system, but I know there's more to it. I would like a deeper understanding of what's going on here. Anything is much appreciated.

• Seems like it would help to know what property you were trying to prove. Jul 28, 2013 at 0:38
• Presumably because whether a body is convex or not does not depend on where it is, so we may as well slide it over so one of its points is at the origin. Or something akin to this. I say "presumably" because I do not know what "a property" is supposed to refer to.
– anon
Jul 28, 2013 at 0:38
• By the way, please see here for a guide to writing math with MathJax, and see here for a guide to formatting posts with Markdown. Jul 28, 2013 at 0:38
• You need $f(x)=x-a$, not $f(a)=x-a$. Jul 28, 2013 at 0:43
• This is a good question but it might help if we could see the example you're referring to. @anon's comment is probably very close to the reason though. Jul 28, 2013 at 0:44