Question
The new figure that results from the transformation of a figure in a plane
Answers
GPT-4o mini
The new figure that results from the transformation of a figure in a plane is commonly referred to as the **image** of the original figure. Transformations can take various forms, including:
1. **Translation**: Moving the figure from one position to another without changing its shape or size.
2. **Rotation**: Turning the figure around a fixed point (the center of rotation) by a certain angle.
3. **Reflection**: Flipping the figure over a line (the line of reflection) to create a mirror image.
4. **Scaling (or Dilation)**: Changing the size of the figure while maintaining its shape, either by enlarging or reducing it.
Each of these transformations can significantly alter the position and orientation of the original figure but will maintain the properties of the figure, such as angles and the relative lengths of sides in the case of Euclidean transformations. The resulting figure is still congruent (for rigid transformations like translation, rotation, and reflection) or similar (for scaling).
1. **Translation**: Moving the figure from one position to another without changing its shape or size.
2. **Rotation**: Turning the figure around a fixed point (the center of rotation) by a certain angle.
3. **Reflection**: Flipping the figure over a line (the line of reflection) to create a mirror image.
4. **Scaling (or Dilation)**: Changing the size of the figure while maintaining its shape, either by enlarging or reducing it.
Each of these transformations can significantly alter the position and orientation of the original figure but will maintain the properties of the figure, such as angles and the relative lengths of sides in the case of Euclidean transformations. The resulting figure is still congruent (for rigid transformations like translation, rotation, and reflection) or similar (for scaling).