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?
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In formal speech or writing, you could say, "The shape is axially symmetric." The symmetry would be sufficient to identify the axis of symmetry (Z). If you were making a formal geometric proof, you might need to provide additional details, like "Z is the axis of symmetry."
As J.R. points out, you could say "X is the mirror image of Y." This is appropriate in both formal and informal contexts. As J.R. points out, it is appropriate in ordinary conversation. It is also appropriate in Physics texts and lectures. Unless you have explicitly defined the concept of a "mirror image", it probably would not be appropriate in a geometric proof.
As Demkemg points out, "axial symmetry" and "bilateral symmetry" are equivalent for 2-D objects. For 3-D objects, "bilateral symmetry" is the same as "mirror" symmetry; both are with respect to a symmetry plane. Also for 3-D objects, "axial symmetry" is the same as "radial symmetry", especially when viewed from a point along the (linear) "axis of symmetry".
2-D is short for "two dimensional" or "planar". 3-D is short for "three dimensional".
"Axial symmetry", "bilateral symmetry", "radial symmetry", "axis of symmetry", and "planar" are all formal. They are appropriate in Physics and Geometry lectures and texts.
"2-D" and "3-D" are informal, and appropriate in ordinary conversation. "Two dimensional" and "three dimensional" are more formal; they sound out of place in many informal conversations.