Final answer:
To determine the scale of the map, form a ratio of 4.2 cm (map distance) to 6.3 km (actual distance), convert km to cm, then simplify to get a scale of 1:150,000.
Step-by-step explanation:
To find the scale of a map where 4.2 cm represents an actual distance of 6.3 km, you start by setting up a ratio that compares the scale distance (the distance on the map) to the actual distance. In this case, we have:
Scale Distance / Actual Distance = 4.2 cm / 6.3 km
To make the units more intuitive, convert the actual distance from kilometers to centimeters (since there are 100,000 centimeters in a kilometer).
6.3 km = 6.3 × 100,000 cm = 630,000 cm
This gives us a new scale ratio:
Scale Distance / Actual Distance = 4.2 cm / 630,000 cm
Finally, to express this as a unit rate, we calculate:
Scale = 4.2 cm / 630,000 cm = 1 / 150,000
Therefore, the scale of the map is 1:150,000.