To determine the actual distance \( d \) between Samantha's school and the park using the map scale, we need to set up the appropriate proportion from the given scale.
The scale of the map is given as \( 0.5 , \text{in.} = 2 , \text{miles} \). This can be expressed as a ratio:
\[ \frac{0.5 , \text{in.}}{2 , \text{miles}} \]
The distance between her school and the park on the map is \( 2.75 , \text{in.} \). We can set up the proportion as follows:
\[ \frac{0.5 , \text{in.}}{2 , \text{miles}} = \frac{2.75 , \text{in.}}{d , \text{miles}} \]
Now, looking at the options provided, the one that matches this setup is:
d over 2 is equal to 0.5 over 2.75
So, the correct proportion that Samantha can use to determine the distance \( d \) is:
\[ \frac{d}{2} = \frac{0.5}{2.75} \]