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)
Responses

shape
shape

distance
distance

angle measure
angle measure

orientation

Answer 1

In the context of transformations, when a rectangle undergoes a translation followed by a dilation, we can analyze the properties:

1. **Shape:** The shape of the rectangle is preserved under both translation and dilation. Translation moves the shape without altering it, and dilation changes the size but not the shape proportions. Therefore, this property is preserved.

2. **Distance:** Translation preserves distances because it moves all points the same way. However, dilation changes the size of shapes, which means distances can change. So, this property is **not preserved** after the transformation.

3. **Angle Measure:** Both translation and dilation preserve angle measures. The angles remain the same in size. Thus, this property is preserved.

4. **Orientation:** Translation maintains the orientation of the shape, but dilation can alter the orientation based on the scale factor. If the dilation factor is negative, the orientation would also be reversed, meaning this property may not be preserved depending on the specific dilation applied.

Based on this analysis, the property that is **NOT preserved after this composition transformation** is **distance** (and potentially **orientation** if the dilation involves a negative scale factor). However, if we strictly choose one property, "distance" is the primary one that is not preserved.