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Which type of isometry is the equivalent of two reflections across intersecting lines?

Rotation


Is line reflection a direct isometry?

if there is an even number of line reflections then yes. if there is n odd number of line reflections, then no.


What is theorem 5.12?

Theorem 5.12- A rotation is a composition of two reflections, and hence is an invertible isometry.


Is reflection always an isometry?

No. While it is true for reflection in a straight line, it is not true for other reflections.


What three transformations have isometry?

The three transformations that have isometry are translations, rotations, and reflections. Each of these transformations preserves the distances between points, meaning the shape and size of the figure remain unchanged. As a result, the original figure and its image after the transformation are congruent.


When the preimage and image are congruent the transformation is called an isometry true or false?

True. An isometry is a transformation that preserves distances and angles, meaning that the preimage and image are congruent. Examples of isometries include translations, rotations, and reflections, all of which maintain the shape and size of geometric figures.


Is a rotation an isometry?

Yes, a rotation is an isometry.


Is a translation an Isometry?

Yes, translation is part of isometry.


What is an isometry?

A isometry is a transformation where distance (aka size) is preserved. In a dilation, the size is being altered, so no, it is not an isometry.


Does an isometry preserves orientation?

An isometry is a transformation that preserves distances between points, and it can either preserve or reverse orientation. For example, a rotation is an isometry that preserves orientation, while a reflection is an isometry that reverses orientation. Therefore, whether an isometry preserves orientation depends on the specific type of transformation being applied.


A preimage and an image are congruent in an isometry?

Yes. Being congruent is part of the definition of an isometry.


What is Isometry?

An isometry is a transformation in which the original figure and its image are congruent. Shape remains constant as size increases.