Assertion: isometry | /r/HasAspect | fixed point
Facets:
Source sentences:
text: Off the top of my head, I suppose given any isometry, you first compose with a translation so that the isometry has a fixed point; then translate the fixed point to the origin; now you are faced with classifying orthogonal transformations of R^2, which falls into two cases depending on whether the determinant is +1 or -1.
text: If an isometry in the plane has more than one fixed point, it is either a reflection (over an axis which crosses that point) or the identity transformation.