Question

1. two circles are dilated, and their radii change from r₁ = 8 to r₂ = 72. identify the scale - factor (k)

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) for two similar figures (here circles are similar) is given by \(k=\frac{\text{new dimension}}{\text{original dimension}}\).

Step2: Substitute the values of radii

Given \(r_1 = 8\) (original radius) and \(r_2=72\) (new radius). Using the formula \(k = \frac{r_2}{r_1}\), we substitute \(r_1 = 8\) and \(r_2 = 72\) into the formula: \(k=\frac{72}{8}\).

Step3: Simplify the fraction

\(\frac{72}{8}=9\)

Answer:

c. 9