Final answer:
The geometry transformation of s(-1,-1) to S(-1,-1) is an identity transformation where the coordinates remain unchanged, meaning no actual transformation has occurred.
Step-by-step explanation:
The transformation of s(-1,-1) to S(-1,-1) does not change the coordinates and thus represents an identity transformation where the point remains fixed and the coordinate system does not change. In the context of rotations in a coordinate system, the general transformations given are:
x' = x cos q + y sin p
y' = -x sin p + y cos p
In the case of an identity transformation, sin p and cos q would equal 0 and 1 respectively, and the point s(-1,-1) would map to itself as S(-1,-1) with no rotation applied. The distance of a point P to the origin is also invariant under identity transformation, and so, the original equation [x² + y²] remains unchanged, demonstrating that point P's distance to the origin is the same before and after the transformation.