To find out how long a line segment would be in the scale drawing to represent 50 miles, you can set up a proportion based on the given scale:
Given that 4 inches represents 100 miles, you can write it as:
\[ \frac{4 \text{ inches}}{100 \text{ miles}} = \frac{x \text{ inches}}{50 \text{ miles}} \]
Now, cross-multiply to solve for \(x\):
\[ 4 \text{ inches} \cdot 50 \text{ miles} = 100 \text{ miles} \cdot x \text{ inches} \]
This simplifies to:
\[ 200 = 100x \]
Then, divide both sides by 100:
\[ x = \frac{200}{100} = 2 \]
So, the line segment that represents 50 miles would be 2 inches long.