what transformation always results in isometery?
The transformation that always results in an isometry is a translation
The transformation that always results in an isometry is a translation.
An isometry is a transformation that preserves distance and angle measures. It means that if you apply an isometry to a geometric figure, the transformed figure will have the same size, shape, and orientation as the original figure.
A translation is a transformation that slides an object from one location to another without changing its shape, size, or orientation. It is achieved by moving every point of the object the same distance in the same direction.
To understand why a translation is an isometry, let’s consider two points A and B in a plane. When we translate the plane by a vector t, point A is moved to A’, and point B is moved to B’. The distance between A and B, which is ∥AB∥, remains the same as the distance between A’ and B’, which is ∥A’B’∥.
Similarly, the angles between the lines connecting A and B, and A’ and B’ are preserved. This is because a translation does not involve any rotation or stretching. It simply shifts the object, maintaining the same distances and angles.
Thus, a translation always results in an isometry, as it preserves both distance and angle measures.
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