Symmetry About Coordinate Axes

This comprehensive page covers the fundamental principles of Symetria osiowa in the coordinate plane, particularly focusing on symmetry about the X and Y axes. The content explores both point and function symmetry with practical examples and essential formulas.

Definition: Symetria względem osi OX i OY refers to the reflection of points and functions across the coordinate axes, where distances and shapes are preserved during transformation.

Example: For a point A$-2,1$, its reflection across the Y-axis (Soy) gives A'(2,1), demonstrating Symetria względem osi OY przykłady.

Highlight: A crucial property of Symetria osiowa is that it preserves both the distance between points and the shape of geometric figures during transformation.

Vocabulary:

• Sox: Symmetry with respect to X-axis
• Soy: Symmetry with respect to Y-axis
• P(x,y): Original point coordinates
• P'$x,-y$: Image point after X-axis reflection
• P'$-x,y$: Image point after Y-axis reflection

Definition: For function transformations:

• Reflection across X-axis: y = -f$x$
• Reflection across Y-axis: y = f$-x$

The page includes detailed coordinate grid illustrations showing multiple examples of point reflections and function transformations, making it an excellent resource for understanding Symetria względem osi OX i OY zadania.