Question

Determine whether the dilation is an enlargement or a reduction.

(1 point)
Responses

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
.
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 .

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.

Answer 1

To determine whether the dilation is an enlargement or a reduction, we need to look at the scale factors mentioned for each case:

1. **AB is a reduction of A′B′ by a scale factor of \( \frac{1}{2} \)**: This means that A′B′ is larger than AB, so it indicates a reduction (AB is smaller).

2. **A′B′ is a reduction of AB by a scale factor of \( \frac{1}{2} \)**: This means AB is larger than A′B′, indicating a reduction (A′B′ is smaller).

3. **AB is an enlargement of A′B′ by a scale factor of \( 2 \)**: This means AB is larger than A′B′, indicating an enlargement (AB is bigger).

4. **A′B′ is an enlargement of AB by a scale factor of \( 2 \)**: This means A′B′ is larger than AB, indicating an enlargement (A′B′ is bigger).

In summary:
- A reduction occurs if the scale factor is less than 1.
- An enlargement occurs if the scale factor is greater than 1.

Based on these principles:
- The statements regarding reductions (1 and 2) are correct about one being a reduction of the other.
- Conversely, statements (3 and 4) indicate enlargements.

To summarize:
- If the scale factor is \( \frac{1}{2} \), this implies a reduction.
- If the scale factor is \( 2 \), this implies an enlargement.

Thus, you can conclude from the cases presented.