1. The problem asks to find the equivalent single dilation scale factor when performing two dilations centered at the origin: first with scale factor 3, then with scale factor \frac{1}{2}. 2. The formula for the composition of dilations centered at the same point is that the overall scale factor is the product of the individual scale factors. 3. Therefore, multiply the two scale factors: $$3 \times \frac{1}{2} = \frac{3}{2}$$ 4. This means performing the two dilations in sequence is equivalent to a single dilation centered at the origin with scale factor $\frac{3}{2}$. 5. In plain language, scaling by 3 and then scaling by half is the same as scaling by one and a half times once.