what transformation always results in isometery?
The transformation that always results in an isometry is called a rigid transformation
The transformation that always results in an isometry is called a rigid transformation.
A rigid transformation preserves the size and shape of a figure, as well as the distances between its points. This means that the transformed figure is congruent to the original figure, making it an isometry.
There are three types of rigid transformations:
1. Translation: This transformation involves sliding a figure without changing its orientation or shape. Every point in the figure moves the same distance and direction. Translations preserve distances and angles, making them isometries.
2. Rotation: This transformation involves turning a figure around a fixed point called the center of rotation. Each point in the figure moves along a circular path, maintaining the same distance from the center. Rotations preserve distances and angles, making them isometries.
3. Reflection: This transformation involves flipping a figure over a line called the line of reflection. Each point in the figure moves to its mirror image across the line, maintaining the same distance. Reflections preserve distances and angles, making them isometries.
It is important to note that a combination of these rigid transformations also results in an isometry. For example, a figure can be translated and then rotated, or reflected and then translated. As long as any combination of translations, rotations, and reflections are performed, the resulting transformation will be an isometry.
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