Final answer:
The question involves mathematical principles to estimate the distance between two points, utilizing the example of calculating the actual distance between two houses on a map using scale conversions.
Step-by-step explanation:
The question pertains to estimating distances, which involves mathematical calculations and understanding units of measurement. In the given statement, distance is being estimated between two points, ranging from the closest point at eighteen inches to the farthest point at four feet. Our understanding of distance measurements has evolved from using human dimensions such as the inch and the yard to more standardized units of measure a practice that became more uniform around the middle of the eighteenth century for the purpose of commerce and international standards.
To solve the example provided where the student asks about the distance from John's house to Mike's house, we would use the map scale provided. First, we need to set up a proportion where 1.5 inches on the map is equal to 2 miles (or 5280 feet x 2) in reality. The actual distance represented on the map is 4.5 inches, so the calculation would be 4.5 inches \(\times\) (10560 feet / 1.5 inches) = 31,680 feet, which is the distance from John's house to Mike's house in feet.