#### What is an isometry?

Answer:Transformations that are isometries :

Type of transformation that is not an isometry :

### Diagrams of Isometries

In the diagram below, both the image and the preimage of $$\triangle ABC $$ have the same dimensions, showing that reflections are isometries.

Again in this diagram, both the image and the preimage of $$\triangle ABC $$ have the same dimensions, showing that translations are isometries.

Lastly, both the image and the preimage of $$\triangle ABC $$ have the same dimensions, showing that rotations are isometries.

#### What is a __direct__ isometry?

Answer:
*and*preserves orientation.

Transformations that are direct isometries :

The type of transformations below are not direct isometries :

### Direct Isometry Diagrams

The animations below show that rotations and translations are direct isometries because the orientation as well as the distance is preserved.

###### Rotation Example

In the animation below, the vetices of $$\triangle ABC $$ are in a clockwise order or orientation, and the same is true for the image after the rotation.

###### Translation Example

Just like the pior animation, the vetices of $$\triangle ABC $$ are in a clockwise order or orientation, and the same is true for the image after the translation.

#### What is an __opposite__ isometry?

Answer:
An opposite isometry preserves distance * but changes * the order, or orientation, from clockwise to counterclockwise, or vice versa.

The one type of transformation that is an opposite isometry is a reflection.

### Opposite Isometry Diagram

###### Reflection Example

The animation below shows that reflections are opposite isometries because the orientation is reversed while the distance is preserved.