what transformation always results in isometery?
rotation,reflection, and translation
The transformation that always results in an isometry is a rigid transformation. A rigid transformation is a transformation that preserves distance and angles. It includes translations, reflections, and rotations.
For example, if we translate or slide a figure in a particular direction without changing its orientation or shape, we can achieve an isometry. Similarly, if we reflect a figure across a line or a point, the resulting image will have the same size and shape as the original figure. Finally, if we rotate a figure about a point or an axis, it can be an isometry if the angle and the direction of rotation are maintained.
In summary, any transformation that does not alter the shape and size of the figure and preserves distance and angles will result in an isometry, which is a type of rigid transformation.
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