An arrow typically exhibits reflectional symmetry, also known as mirror symmetry. This means that if you were to draw a line down the center of the arrow, the two halves would be mirror images of each other. Arrows do not usually have rotational symmetry, as rotating them around a point would not result in the same shape.
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An arrow (→) has one line of symmetry. A double-headed arrow (↔) has two lines of symmetry and rotational symmetry if you want to claim it.
The line of symmetry in an arrow is the line connecting to the > part of the arrow.
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Along the length of the arrow, probably 2 - possibly 3. Otherwise there is no rotational symmetry.
If we are talking about a normal arrow, then no. if " -> " is rotated 90 degrees, it would not look the same as it did before. It would look something like this: ^ | Which would not be the same.