Question

1. the diameters of two circles are 12 and 36. what scale factor (k) is needed to map the smaller circle onto the larger circle? a. 2.5 b. 2 c. 3 d. 1.5

Explanation:

Step1: Recall scale - factor formula

The scale factor \(k\) from a smaller figure to a larger figure is given by \(k=\frac{\text{dimension of larger figure}}{\text{dimension of smaller figure}}\).

Step2: Identify the dimensions

The diameter of the smaller circle is \(d_1 = 12\) and the diameter of the larger circle is \(d_2=36\).

Step3: Calculate the scale factor

\(k=\frac{d_2}{d_1}=\frac{36}{12}=3\)

Answer:

c. 3