# 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.

### What is preserved in a reflection?

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.#### What is preserved in a rigid motion?

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).#### What is a rigid motion in math?

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.#### Which transformation preserves only angle measurement?

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.

B.

### Is a dilation is an isometry?

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.#### What does an isometric transformation preserve?

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.#### What is not a rigid transformation?

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.#### What happens when you dilate a line?

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