Question

1. two circles have radii r₁ = 4 and r₂ = 36. what is the scale factor (k) for the dilation that maps the smaller circle onto the larger circle? a. 7 b. 8 c. 10 d. 9

Explanation:

Step1: Recall the formula for scale factor

The scale factor \( k \) for dilation is given by \( k=\frac{\text{radius of image}}{\text{radius of pre - image}}\).

Step2: Identify the radii

The radius of the smaller circle (pre - image) \(r_1 = 4\) and the radius of the larger circle (image) \(r_2=36\).

Step3: Calculate the scale factor

Substitute the values into the formula: \(k=\frac{r_2}{r_1}=\frac{36}{4}=9\).

Answer:

d. 9