Question

1 find the scale factor that was used to dilate figure i to create figure ii. was the dilation an enlargement or reduction? 24 cm figure i 16 cm figure ii

Explanation:

Step1: Recall scale factor formula

The scale factor \( k \) for dilation is the ratio of the length of a side in the image (Figure II) to the length of the corresponding side in the original figure (Figure I). So \( k=\frac{\text{Length of Figure II}}{\text{Length of Figure I}} \).

Step2: Substitute values

Length of Figure I is \( 24 \, \text{cm} \), length of Figure II is \( 16 \, \text{cm} \). So \( k = \frac{16}{24}=\frac{2}{3} \).

Step3: Determine enlargement/reduction

Since \( 0 < k < 1 \) (here \( k = \frac{2}{3}\approx0.67 \)), the dilation is a reduction.

Answer:

The scale factor is \(\frac{2}{3}\), and the dilation is a reduction.