1. Giovanni went to Los Angeles, California, for the summer to visit his cousins. He used a map of bus routes to get from the airport to his cousin’s house. The distance from the airport to his cousin’s house is 56 km. On his map, the distance is 4 cm. What is the scale factor?
56 / 4 = 14
1 cm = 14 km
To find the scale factor, we need to determine the ratio between the distance on the map and the actual distance in reality.
Given that the distance on the map is 4 cm and the actual distance is 56 km, we can set up a proportion to find the scale factor:
actual distance / distance on the map = scale factor
Plugging in the values we have, the proportion becomes:
56 km / 4 cm = scale factor
Simplifying this equation, we have:
(56 km / 4 cm) = scale factor
Converting the units to match (1 km = 10,000 cm), we get:
(56 km / 10,000 cm) / (4 cm / 1) = scale factor
Simplifying further, we have:
(56 / 10,000) / (4 / 1) = scale factor
Now, calculating this expression, we get:
0.0056 / 4 = scale factor
So, the scale factor is 0.0014.
The scale factor indicates that for every 1 cm on the map, the corresponding distance in reality is 0.0014 km.