transforms the point P(x;y) into the point P'(-x;y): Sy is a
symmetry with respect to the ordinate axis.
transforms the point P(x;y) into the point P'(x;-y): Sx is a
symmetry with respect to the abscissa axis.
A geometric linear transformation
transforms the point P(x;y) into the point P'(kx;ky): S is a
homothety with center at O.
- H multiplies by k the lengths of the segments: k is the homothety ratio.
- In particular, if k=1 H is the identity, if k = -1 H is a symmetry with respect to O.
- Homotheties do not change the slopes of the transformed straight lines, therefore the homothetic polygons have angles ordinately congruent.
A geometric linear transformation
rotates the point P(x;y) by an angle α: R is a
rotation with center at O.
Rotations transform the segments into segments with equal length: therefore they are isometries.
The composition of a rotation with a homothety is a similarity with center at O:
