What is an example of Isometry?
Isometry. A transformation that is invariant with respect to distance. That is, the distance between any two points in the pre-image must be the same as the distance between the images of the two points. Isometries: Reflections, rotations, translations, glide reflections.
A reflection is called a rigid transformation or isometry because the image is the same size and shape as the pre-image. The reflection line, m, is the perpendicular bisector of the segments joining each point to its image. Properties preserved under a line reflection from the pre-image to the image.
- The concepts of congruence, similarity, and symmetry can be understood from the perspective of geometric transformation. Fundamental are the rigid motions: translations, rotations, reflections, and combinations of these, all of which are here assumed to preserve distance and angles (and therefore shapes generally).
- A rigid motion of the plane ( or an isometry ) is a motion which preserves distance. There are four basic rigid motions: (1) Reflection. (2) Glide Reflection. (3) Rotation.
- As the sticker rotates around the center of the tire, its shape does not change, so the star's side lengths and angle measurements are unchanged. In general, when we rotate a shape about a point, we preserve length and angle measurement, so rotation is a rigid transformation.
An isometry, such as a rotation, translation, or reflection, does not change the size or shape of the figure. A dilation is not an isometry since it either shrinks or enlarges a figure. An isometry is a transformation where the original shape and new image are congruent.
- An isometric transformation (or isometry) is a shape-preserving transformation (movement) in the plane or in space. The isometric transformations are reflection, rotation and translation and combinations of them such as the glide, which is the combination of a translation and a reflection.
- There are four main types of transformations: translation, rotation, reflection and dilation. These transformations fall into two categories: rigid transformations that do not change the shape or size of the preimage and non-rigid transformations that change the size but not the shape of the preimage.
- When a figure is dilated, a segment (side) of the pre-image that does not pass through the center of dilation will be parallel to its image. Concept 3: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Updated: 3rd September 2018