Question

1. find the scale factor that was used to dilate figure a to create figure b. was the dilation an enlargement or reduction? figure a has a side of 30 m and another of 25 m. figure b has a side of 18 m and another of 15 m.

Explanation:

Step1: Identify corresponding sides

We take the length of a side from Figure A and the corresponding side from Figure B. Let's use the side of length 30 m in Figure A and 18 m in Figure B, or 25 m in Figure A and 15 m in Figure B.

Step2: Calculate scale factor

The scale factor \( k \) is the ratio of the length of a side in Figure B to the length of the corresponding side in Figure A. Using the sides 30 m (A) and 18 m (B): \( k=\frac{18}{30}=\frac{3}{5} = 0.6\). Using 25 m (A) and 15 m (B): \( k=\frac{15}{25}=\frac{3}{5}=0.6\).

Step3: Determine enlargement or reduction

Since the scale factor \( 0.6<1 \), the dilation is a reduction.

Answer:

Scale factor: \(\frac{3}{5}\) (or 0.6); Dilation: reduction