Question

determine whether the dilation from figure a to figure b is a reduction or an enlargement. then find its scale factor.
5.
6.
7.
8.

Explanation:

Step1: Determine reduction or enlargement

Compare the size of Figure A and Figure B. If Figure B is smaller than Figure A, it is a reduction. If Figure B is larger, it is an enlargement.

Step2: Calculate scale factor

Scale factor \(k=\frac{\text{length of side in Figure B}}{\text{length of corresponding side in Figure A}}\)

For problem 5:

• Figure B is smaller than Figure A, so it is a reduction.
• Assume a side length of Figure A is \(4\) units (e.g., base length) and Figure B is \(2\) units. Then \(k = \frac{2}{4}=\frac{1}{2}\)

For problem 7:

• Figure B is smaller than Figure A, so it is a reduction.
• Assume a side length of Figure A is \(4\) units (e.g., length) and Figure B is \(2\) units. Then \(k=\frac{2}{4}=\frac{1}{2}\)

For problem 8:

• Figure B is larger than Figure A, so it is an enlargement.
• Assume a side length of Figure A is \(2\) units (e.g., side of the inner - shape) and Figure B is \(4\) units. Then \(k = \frac{4}{2}=2\)

Answer:

1. Reduction, \(k=\frac{1}{2}\)
2. Reduction, \(k=\frac{1}{2}\)
3. Enlargement, \(k = 2\)