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
- Px,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 = -fx
- 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.
