This is strongly related to Usage of "symmetrical" and "symmetric" but with a slightly different flavor and not answered within that question.

If I wish to indicate that X is the reflection of Y do I say "X is symmetrical to Y" or "X is symmetric to Y"? The context is mathematical, yes.

Google finds about five times as many occurrences of "symmetrical to" but that, of course, proves nothing.

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    What makes you think one of those is right and one of them wrong? – tchrist Dec 28 '16 at 16:29
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    Both forms do in fact occur relatively frequently, but note that (a) - with has always been more likely than to, and (b) - the shorter form symmetric has come to dominate in recent decades. – FumbleFingers Dec 28 '16 at 16:32
  • @tchrist I do not think one of them is wrong but I'm pretty sure one of them is preferable to the other =) – imakhlin Dec 28 '16 at 16:33
  • @FumbleFingers Could you please elaborate? Google says: "is symmetrical to point" -- 20600 results, "is symmetric to point" -- 8,930 results, "is symmetrical with point" -- 4, "is symmetric with point" -- 6. Once again, I understand that this doesn't prove a thing but it does seem very odd in view of your claims. – imakhlin Dec 28 '16 at 16:41
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    The first point to note is that symmetric and symmetrical are effectively synonyms for most purposes (but as answers to the earlier indicate, the former has recently become far more common in technical contexts). But when considering a specific context such as yours, I personally wouldn't be likely to use either version in respect of a single ""point". I might perhaps say Shape A is symmetric with Shape B, but then I'd say Point X on A corresponds to Point Y on B. That's to say I normally think of symmetry as applying to complete (""reversible") shapes, not points. – FumbleFingers Dec 28 '16 at 16:59

A Google Ngram chart of "is symmetric to" (blue line) vs. "is symmetrical to" (red line) vs. "is symmetric with (green line) vs. "is symmetrical with" (yellow line) for the period 1800–2005, with smoothing 3, looks like this:

But a check of the actual matches associated with both the "is symmetric with" and "is symmetrical with" lines indicates that they are dominated by matches of the form "is symmetric/symmetrical with respect to ..." which is not the type of construction that the OP asks about. Dropping those to wordings from the chart, we get this magnified chart for "is symmetric to" (blue line) vs. "is symmetrical to" (red line), for the same time period, with the same smoothing:

This chart suggests that for much of the past century the "symmetrical" variant has been somewhat more popular than the "symmetric" variant—but that the situation has changed in recent years. At this point, usage of the two variants in published content appears to be so close that it would be difficult to argue that either form is wrong. Under the circumstances, unless I were under orders to follow an in-house word-list spelling preference, I would simply adopt the form I preferred, use it consistently, and not look back.

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A point cannot be symmetric or symmetrical to another point.

Their positioning can be symmetric(al). Together they can form a symmetric pattern (e.g., symmetric about a mirror line or plane).

These (essentially synonymous) words mean "Having similarity in size, shape, and relative position of corresponding parts" (WordWeb Online). But a point has no parts, size, or shape.

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