Geometric Transformations in the Plane
This page provides a comprehensive overview of various transformations du plan in geometry, including symmetry, translation, rotation, and homothety. Each transformation is explained with its key characteristics and methods of construction.
Definition: Transformation du plan refers to geometric operations that change the position, size, or orientation of figures in a plane while preserving certain properties.
The page begins with an explanation of axial symmetry (symétrie axiale).
Vocabulary: Symétrie axiale is a transformation where a figure is reflected across a line, creating a mirror image.
It is described as a "folding" or superposition process, typically constructed using tools such as a ruler, set square, or compass.
Next, the document introduces central symmetry (symétrie centrale).
Definition: Symétrie centrale is a transformation where a figure is rotated 180 degrees around a fixed point.
This is described as a half-turn around a center point and can be constructed using a ruler and compass.
The page then moves on to translation, which is represented by a vector.
Highlight: In a translation, all points of a figure move in the same direction and by the same distance.
Rotation is another transformation discussed, described as turning around a center point by a specific angle and direction.
Example: A rotation of 50° is illustrated in the document, showing how a point moves around a center.
Finally, the page covers homothety (homothétie).
Definition: Homothétie is a transformation that enlarges or reduces a figure from a center point by a specific ratio.
An example is given where A'B' = 3 x AB, indicating an enlargement.
The document includes various diagrams and notations to illustrate these concepts, making it a valuable resource for students studying transformations géométriques in mathematics.
