Homothétie is a geometric transformation that enables scaling of geometric figures through enlargement or reduction. This fundamental mathematical concept operates with a center point and a ratio, creating precise geometric relationships.
- The transformation involves a center point O and a ratio k that determines whether the figure is enlarged (k>0) or reduced (k<0)
- When k>0, the resulting figure maintains the same orientation as the original
- When k<0, the transformed figure appears on the opposite side of point O
- Special cases include k=1 (superimposed figures) and k=-1 (central symmetry)
- The homothétie transformation géométrique preserves the shape's angles and proportions while changing its size
