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 . 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 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.
Answers
Answered by
GPT-4o mini
To determine whether a dilation is an enlargement or a reduction, we look at the scale factor:
- If the scale factor is greater than 1, it is an enlargement.
- If the scale factor is less than 1 but greater than 0, it is a reduction.
Let's analyze the statements provided:
1. **AB is a reduction of A′B′ by a scale factor of \( \frac{1}{2} \)**.
- Here, \( \frac{1}{2} < 1 \), indicating that AB is smaller than A′B′. Thus, it is a **reduction**.
2. **A′B′ is a reduction of AB by a scale factor of \( \frac{1}{2} \)**.
- This statement is inverse to the first and also means \( A′B′ \) is smaller than \( AB \), confirming it is also a **reduction**.
3. **A′B′ is an enlargement of AB by a scale factor of 2**.
- Here, the scale factor of 2 is greater than 1, indicating that A′B′ is larger than AB. Thus, this represents an **enlargement**.
4. **AB is an enlargement of A′B′ by a scale factor of 2**.
- This statement is the inverse of the third, implying that AB is larger than A′B′, confirming it is also an **enlargement**.
From this analysis, we can conclude:
- Statements referring to a scale factor of \( \frac{1}{2} \) indicate **reductions**.
- Statements referring to a scale factor of 2 indicate **enlargements**.
In summary:
- A reduction occurs when the scale factor is \( \frac{1}{2} \) (as given in the first and second statements).
- An enlargement occurs when the scale factor is 2 (as stated in the third and fourth statements).
- If the scale factor is greater than 1, it is an enlargement.
- If the scale factor is less than 1 but greater than 0, it is a reduction.
Let's analyze the statements provided:
1. **AB is a reduction of A′B′ by a scale factor of \( \frac{1}{2} \)**.
- Here, \( \frac{1}{2} < 1 \), indicating that AB is smaller than A′B′. Thus, it is a **reduction**.
2. **A′B′ is a reduction of AB by a scale factor of \( \frac{1}{2} \)**.
- This statement is inverse to the first and also means \( A′B′ \) is smaller than \( AB \), confirming it is also a **reduction**.
3. **A′B′ is an enlargement of AB by a scale factor of 2**.
- Here, the scale factor of 2 is greater than 1, indicating that A′B′ is larger than AB. Thus, this represents an **enlargement**.
4. **AB is an enlargement of A′B′ by a scale factor of 2**.
- This statement is the inverse of the third, implying that AB is larger than A′B′, confirming it is also an **enlargement**.
From this analysis, we can conclude:
- Statements referring to a scale factor of \( \frac{1}{2} \) indicate **reductions**.
- Statements referring to a scale factor of 2 indicate **enlargements**.
In summary:
- A reduction occurs when the scale factor is \( \frac{1}{2} \) (as given in the first and second statements).
- An enlargement occurs when the scale factor is 2 (as stated in the third and fourth statements).
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