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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.
Which of the following properties refers to the corresponding side lengths of the preimage and image in an isometry?
distance
Which properties are not preserved by an isometry?
An isometry preserves distances and angles between points, meaning that the shape and size of geometric figures remain unchanged. However, it does not necessarily preserve properties such as orientation (e.g., a reflection changes the orientation) or the position of points in space (e.g., a translation moves points). Additionally, while the overall configuration may remain intact, specific coordinates of points may change.
Is a rotation an isometry?
Yes, a rotation is an isometry.
Is a translation an Isometry?
Yes, translation is part of 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.
Which of these properties are not preserved by a dilation?
distance
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.
Explain why a glide reflection is an isometry?
Because the glide reflection is a combination of two isometries, it is also an isometry.
An isometry can be illustrated with a graphing calculator. Which function rule matches the isometry?
(x,y) (-x,-y)
Which transformation is not an isometry?
Dilation.
