Understanding Isometries | Translation, Rotation, and Reflection as Rigid Transformations

what transformation always results in isometery?

An isometry is a transformation that preserves distances and angles between objects

An isometry is a transformation that preserves distances and angles between objects. There are three types of transformations that always result in an isometry:

1. Translation: A translation is a transformation that slides an object without changing its size or shape. It moves every point of the object the same distance and direction. Since the distances between any two points on the object are preserved, translations are considered isometries.

2. Rotation: A rotation is a transformation that turns an object around a fixed point, called the center of rotation. It preserves the size and shape of the object. Since the angles between any two intersecting lines or line segments on the object are preserved, rotations are considered isometries.

3. Reflection: A reflection is a transformation that flips an object over a fixed line, called the line of reflection. It creates a mirror image of the object. Reflections preserve distances between any two points on the line of reflection, as well as the angles between intersecting lines or line segments perpendicular to the line of reflection. Therefore, reflections are also considered isometries.

These three transformations (translation, rotation, and reflection) are known as rigid transformations because they preserve the size and shape of the object being transformed.

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