Question

Rectangle ABCD, with four 90 degree angles, undergoes a translation followed by a dilation. Which of the following properties are not perserved after this composition transformation? A: orientation B: angle measure C: distance D:shape

Answer 1

When a rectangle undergoes a translation followed by a dilation, we can analyze the properties in question:

1. **Translation**: This transformation moves every point of the rectangle the same distance in a specified direction. During translation, the following properties remain preserved:
- **Orientation**: This is preserved because the order of the vertices remains the same.
- **Angle measure**: The angles of the rectangle (90 degrees) remain unchanged.
- **Distance**: The distances (lengths of sides) between points remain unchanged during translation.
- **Shape**: The shape of the rectangle remains the same.

2. **Dilation**: This transformation enlarges or reduces the figure proportionally from a center point. The properties affected are:
- **Orientation**: This is still preserved after dilation.
- **Angle measure**: The angles of the rectangle (still 90 degrees) remain unchanged.
- **Distance**: The lengths of the sides change, so distances are not preserved.
- **Shape**: The shape remains similar but may be larger or smaller.

Given these transformations, let's evaluate the properties:

- **A: Orientation**: Preserved (remains the same).
- **B: Angle measure**: Preserved (each angle remains 90 degrees).
- **C: Distance**: Not preserved (distances change after dilation).
- **D: Shape**: Preserved in the sense that it remains a rectangle, but the size changes.

In conclusion, the property that is **not preserved** after the composition of a translation followed by a dilation is:

**C: distance**.