# X is axially symmetric to Y with respect to Z

In the following figure, is it automatically correct and clear to say that

X is axially symmetric to Y with respect to Z

?

Is there any better way to express this fact?

• This is one of those "dangerously close to proofreading questions." :^) As for "Is there any better way to express it?" that depends on your audience. In a bar talking with friends, I might say, "X is the mirror image of Y." When giving a technical presentation at a conference, though, your wording might be better – not because the words are "fancier," but because they are more mathmatically precise. In short, axially symmetric is understandable, but rather atypical in everyday conversation.
– J.R.
Nov 15, 2014 at 23:45
• @J.R. Thanks, I understand. I haven't done much geometric in English so I wasn't very confident :) I guess the border between word usage and proofreading is narrow! Nov 15, 2014 at 23:49
• Z is a line of symmetry for X and Y.
– Jim
Nov 16, 2014 at 7:36
• I think saying the shape has reflection symmetry, or the shape is bilaterally symmetric is a better choice. Saying axially symmetric, though applicable, usually implies three-dimensional objects. Nov 16, 2014 at 9:10
• @Franck: As for the narrow line between word usage and proofreading, you can always make that a wider boundary by doing and including more research. Questions like "Does this sound okay?" sound like a request for proofreading. Questions with supporting research (such as, "I know this phrase is commonly used, because I found more than 300,000 instances on Google; however, I'm wondering if those words sound too scientific, or if they are readily understandable") sound like a question from someone who knows what they want, has done their homework, and still needs some guidance or help.
– J.R.
Nov 17, 2014 at 10:23