Which of the following represents the straight-line distance between any two points on a map?

The correct answer is the azimuthal projection. This type of map projection displays the surface of the Earth in such a way that it preserves the straight-line distance from a central point to any other point on the map. This means that if you were to draw a straight line between two locations on an azimuthal map, that line would accurately reflect the shortest distance between those points on the Earth's surface.

Azimuthal projections are particularly useful for applications where calculating precise distances from a specific central point is important, such as in navigation or flight planning. The projection allows for better accuracy in distance measurements compared to other types of map projections that may distort distances.

In contrast, the Mercator projection, while it maintains straight lines for navigation, distorts size and shape, especially as one moves toward the poles, making it less reliable for measuring straight-line distances over longer routes. Choropleth maps focus on representing statistical data through color gradients rather than physical distances. Flow-line maps illustrate movement or flow between places but do not provide a means to measure direct distances accurately. Thus, the azimuthal projection stands out as the correct representation of straight-line distances between points on a map.