Question

A trapezoid ABCD undergoes some different transformations.

Determine which transformations listed below result in a congruent trapezoid, A'B'C'D'.

Drag each transformation on the left to indicate whether it is either congruent or not congruent to ABCD.

Choices

A translation of 6 units down and 3 units to the right
A dilation by a factor of 2, centered at the origin
A 180o rotation counterclockwise about the origin
A reflection across the y-axis
Answers

Congruent to ABCD
Not Congruent to ABCD

Answer 1

To determine whether the transformations result in a congruent trapezoid A'B'C'D', we analyze each transformation one by one:

1. **A translation of 6 units down and 3 units to the right**:
- **Congruent to ABCD**.
- Translations preserve the shape and size of the figure.

2. **A dilation by a factor of 2, centered at the origin**:
- **Not Congruent to ABCD**.
- Dilation changes the size of the figure, hence creating a similar figure, but not congruent.

3. **A 180° rotation counterclockwise about the origin**:
- **Congruent to ABCD**.
- Rotations preserve the shape and size of figures.

4. **A reflection across the y-axis**:
- **Congruent to ABCD**.
- Reflections also preserve the shape and size of figures.

So, the classifications are as follows:

- A translation of 6 units down and 3 units to the right: **Congruent to ABCD**
- A dilation by a factor of 2, centered at the origin: **Not Congruent to ABCD**
- A 180° rotation counterclockwise about the origin: **Congruent to ABCD**
- A reflection across the y-axis: **Congruent to ABCD**