if there is an even number of line reflections then yes. if there is n odd number of line reflections, then no.
No. While it is true for reflection in a straight line, it is not true for other reflections.
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.
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.
Not always
Rotation
if there is an even number of line reflections then yes. if there is n odd number of line reflections, then no.
Theorem 5.12- A rotation is a composition of two reflections, and hence is an invertible isometry.
No. While it is true for reflection in a straight line, it is not true for other reflections.
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.
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.
Yes, a rotation is an isometry.
Yes, translation is part of 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.
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.
Yes. Being congruent is part of the definition of an isometry.
An isometry is a transformation in which the original figure and its image are congruent. Shape remains constant as size increases.