Question

Use the image to answer the question. Determine whether the dilation is an enlargement or a reduction. (1 point) Responses AB¯¯¯¯¯¯¯¯ 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. 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. 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 a reduction of AB¯¯¯¯¯¯¯¯ by a scale factor of 12 . A'B' is -4,-1 AB is -2,-0.5

Answer 1

To determine whether the dilation is an enlargement or a reduction, we need to compare the lengths of the segments AB and A'B' and also examine their coordinates.

Given the coordinates:
- \( A'(-4, -1) \)
- \( B' \) (not specified, assuming it’s obtained based on the scale or similarity)
- \( A(-2, -0.5) \)

### Step 1: Calculate the lengths of the segments

1. **Find the length of AB:**
- If \( B \) needs to be provided for a calculation, here we assume some undefined coordinates for \( B \) would make the computation valid based on context, but you mentioned only \( A' \) and \( A \).

2. **Find the length of A'B':**
- Similarly, this length cannot be directly obtained without a second point for \( B' \).

### Step 2: Determine the Scale Factor

If we are using specific coordinates, the scale factor can generally be calculated as follows:

\[
\text{Scale Factor} = \frac{\text{Length of image (A'B')}}{\text{Length of original (AB)}}
\]

If the ratio is greater than 1, it is an **enlargement**. If it is less than 1, it is a **reduction**.

### Provided Statements

From the statements, we can analyze the options which relate terms:
- AB is an enlargement of A'B' by a scale factor of 2 suggests:
- `Length of AB = 2 * Length of A'B'` – indicates AB is longer than A'B'.

- A'B' is a reduction of AB by a scale factor of 1/2 supports:
- `Length of A'B' = 1/2 * Length of AB` – again indicating A'B' is shorter than AB.

#### Conclusion:
Given the above context, and if we take for granted that there’s no contradiction in segments as per coordinates, the relation holds as AB > A'B'.

We confirm:
- **AB is an enlargement** of A'B' with a scale factor of 2.
Thus, referring to the question of whether the dilation is an enlargement or a reduction, **it is an actual enlargement** based on the context of points implying that AB spans more than A'B'.