Reflection, rotation, and translation are fundamental types of geometric transformations that move a figure on a plane without changing its size or shape. They are often referred to as rigid transformations or isometries.
Reflection
A reflection flips the figure over a line to create a mirror image.
- Action: Creates a mirrored copy.
- Key Element: The line of reflection. Every point in the original figure is the same distance from the line as the corresponding point in the reflected figure.
- Example: Reflecting a letter 'P' over a vertical line results in a reversed 'P'.
Rotation
A rotation turns the figure around a point.
- Action: Pivots the figure.
- Key Elements: The center of rotation and the angle of rotation. The center of rotation is the point the figure turns around, and the angle specifies how much it turns.
- Example: Rotating a square 90 degrees clockwise around its center point.
Translation
A translation slides the figure to a different location.
- Action: Moves the figure without turning or flipping it.
- Key Element: The translation vector or direction and distance. Every point in the original figure moves the same distance in the same direction.
- Example: Sliding a triangle 5 units to the right and 3 units up.
Here is a simple comparison of these three transformations:
| Transformation | Description (from Reference) | Action | Key Element(s) | Effect |
|---|---|---|---|---|
| Reflection | flips the figure over a line to create a mirror image | Flips | Line of reflection | Creates a mirror image |
| Rotation | turns the figure around a point | Turns/Pivots | Center & angle of rotation | Changes orientation |
| Translation | slides the figure to a different location | Slides | Direction & distance | Changes location, preserves orientation |
These basic transformations are essential concepts in geometry, graphics, and physics, describing how objects move and interact in space.
