Can a boolean value concerning changing the sign or not of a scalar value considered a 1D rotation?

Question

So going descending order on dimensions:

3D: 3 scaling scalars, 3 rotation scalars, 3 translation scalars

2D: 2 scaling scalars, 1 rotation scalars, 2 translation scalars

1D: 1 scaling scalar, 1 rotation boolean (?), 1 translation scalar

The reason I'm asking about 1D Rotation being a boolean is because one can make a point jump across a pivot(P), the origin or other value. The second example in the image, with P on 1, has the conjugation:
-1 -(P) = -2: <=> (-)-2 = 2 <=> 2 + (P) = 3

So could changing the sign considered a 1D rotation?

Thank you!

Answer 1

The set of rotations can be described by the set of orthogonal matrices (i.e. matrices such that $A^T = A^{-1}$) with determinant $1$.

An orthogonal matrix with determinant $-1$ is an improper rotation or a reflection combined with a rotation

So, in the sense of this definition, you'd consider it a reflection, since the matrix would be $A=[-1]$ which has determinant $-1$.