Question

Rectangle ABCD with four 90° angles, undergoes and translation followed by a dilation.
Which of the following properties are NOT preserved after this composition transformation?
(1 point)
angle measure
orientation
shape
distance

Answer 1

In the composition of a translation followed by a dilation, the following properties are preserved:

1. **Angle measure**: This is preserved because both translation and dilation do not change the angles of the shape.
2. **Shape**: This is also preserved because a dilation is a type of similarity transformation that maintains the shape of the figure, though it can change the size.
3. **Distance**: This property is not preserved during dilation, as dilation changes the distances between points (scales them by a certain factor). However, translation preserves distances.

The property that is **NOT preserved** in this transformation is:

- **Orientation**: While translation preserves orientation, dilation can reverse it depending on the factor and center of dilation. Therefore, in general, the overall composition can lead to a change in orientation.

Based on this analysis, the properties that are NOT preserved are:

- Distance (specifically due to dilation)
- Orientation

In summary, while angle measure and shape are preserved through both transformations, the orientation and the exact distances may change.