what transformation always results in isometery?
A transformation that always results in an isometry is a rigid transformation
A transformation that always results in an isometry is a rigid transformation. Rigid transformations preserve the shape and size of an object, meaning that the distances between points remain the same.
There are three main types of rigid transformations:
1. Translation: This transformation involves moving an object without changing its shape or size. In a translation, every point on the object is shifted the same distance and in the same direction.
2. Rotation: This transformation involves rotating an object around a fixed point called the center of rotation. The shape and size of the object remain unchanged, but its orientation is altered.
3. Reflection: This transformation involves flipping an object over a line of reflection. The object is reflected across the line, resulting in a mirror image. The shape and size of the object remain the same.
All three of these rigid transformations preserve distances between points, which is why they are considered isometries. Other transformations, such as dilation or shear, change the size or shape of an object and are not isometries.
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