Question

Determine whether the dilation is an enlargement or a reduction.(1 point)ResponsesAB¯¯¯¯¯¯¯¯ is an enlargement of A′B′¯¯¯¯¯¯¯¯¯¯ by a scale factor of 2.Modifying above upper A upper B with bar  is an enlargement of  Modifying above upper A prime upper B prime with bar  by a scale factor of 2.AB¯¯¯¯¯¯¯¯ is a reduction of A′B′¯¯¯¯¯¯¯¯¯¯ by a scale factor of 12.Modifying above upper A upper B with bar  is a reduction of  Modifying above upper A prime upper B prime with bar  by a scale factor of  Start Fraction 1 over 2 End Fraction .A′B′¯¯¯¯¯¯¯¯¯¯ is an enlargement of AB¯¯¯¯¯¯¯¯ by a scale factor of 2.Modifying above upper A prime upper B prime with bar  is an enlargement of  Modifying above upper A upper B with bar  by a scale factor of 2.A′B′¯¯¯¯¯¯¯¯¯¯ is a reduction of AB¯¯¯¯¯¯¯¯ by a scale factor of 12.Modifying above upper A prime upper B prime with bar  is a reduction of  Modifying above upper A upper B with bar  by a scale factor of  Start Fraction 1 over 2 End Fraction .

Answer 1

To determine whether a dilation is an enlargement or a reduction based on the scale factor, we can use the following rules:

- If the scale factor is greater than 1, the dilation is an **enlargement**.
- If the scale factor is less than 1 (but greater than 0), the dilation is a **reduction**.

Now let's analyze the responses:

1. **AB is an enlargement of A′B′ by a scale factor of 2.**
- Scale factor: 2 (greater than 1) ➔ This is an **enlargement**.

2. **AB is a reduction of A′B′ by a scale factor of 12.**
- Scale factor: 12 (greater than 1) ➔ This statement is incorrect because it states a reduction with a scale factor greater than 1.

3. **A′B′ is an enlargement of AB by a scale factor of 2.**
- Scale factor: 2 (greater than 1) ➔ This is an **enlargement**.

4. **A′B′ is a reduction of AB by a scale factor of 12.**
- Scale factor: 12 (greater than 1) ➔ This statement is incorrect because it states a reduction with a scale factor greater than 1.

5. **AB is a reduction of A′B′ by a scale factor of 1/2.**
- Scale factor: 1/2 (less than 1) ➔ This is a **reduction**.

6. **A′B′ is a reduction of AB by a scale factor of 1/2.**
- Scale factor: 1/2 (less than 1) ➔ This is a **reduction**.

From the analysis, the correct classifications based on the provided scale factors are:

1. Enlargement (scale factor of 2)
3. Enlargement (scale factor of 2)
5. Reduction (scale factor of 1/2)
6. Reduction (scale factor of 1/2)

The statements that are correct with their classifications are:

- **Enlargement by a scale factor of 2**
- **Reduction by a scale factor of 1/2**

The incorrect statements are those suggesting a reduction with a scale factor greater than 1.