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.