direction
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.
distance
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.
Yes, a rotation is an isometry.
Yes, translation is part of isometry.
distance
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.
Because the glide reflection is a combination of two isometries, it is also an isometry.
(x,y) (-x,-y)
Dilation.