Assertion: isometry's point | /r/HasProperty | fixed
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: All points end up where they started, so all points are fixed points.
text: If all the points of k are fixed, then this is called a line of fixed points; it is invariant, also, but more more.