Map Projections and Distortion Questions and Answers

Answer: C

Over the small area a single sheet covers, keeping angles and local shape true means that features and bearings can be worked with directly. Area distortion over so small an extent is negligible, so nothing is given up by choosing conformality here.

Answer: D

An azimuthal projection in polar aspect places the point of contact at the pole, so distortion grows outward evenly and directions from the centre are true. A normal cylindrical projection is at its worst exactly there.

Answer: A

The line of contact lies at the Equator, so scale error increases with latitude and the poles cannot be shown at all. The same projection is perfectly reasonable for an equatorial band, where the line of contact runs straight through the area of interest.

Answer: B

Web Mercator keeps the conformality that makes local shapes look right at high zoom and makes square tiles convenient. It inherits the area exaggeration too, which is why global comparisons made on web maps are misleading.

Answer: C

Correct answer: It exaggerates area at high latitudes

That is the genuine and unavoidable criticism, inherited from Mercator: Greenland appears comparable to Africa when it is about a fourteenth its size. The other three are not faults of it - local shapes are essentially preserved, cities are shown correctly at the scales the web uses it for, and its whole virtue for navigation is that a constant bearing is a straight line.

Answer: D

Correct answer: the purpose, the extent and the shape of the area

What the map is for decides the property that must be preserved - area for statistical comparison, angle for navigation and large-scale survey, distance from a point for range maps. The extent decides how much distortion is unavoidable, and the shape of the area decides the family and aspect: a cone for a mid-latitude region wider than it is tall, a transverse cylinder for one long north to south.

Answer: A

Flattening a curved surface must stretch it somewhere, so the cartographer decides which property to protect and where to put the error rather than whether to have any. That choice is the substance of projection selection.

Answer: B

Correct answer: A way of representing a curved surface on a flat one

A projection is a systematic transformation from positions on the ellipsoid to positions on a plane. Because a curved surface cannot be flattened without distortion, every projection distorts something, and the whole subject consists of choosing which distortion to accept and where to put it.

Answer: C

Correct answer: A sphere

A cone and a cylinder are developable surfaces: each can be cut and unrolled flat without stretching or tearing, which is why they serve as intermediate surfaces in projection. A sphere is not, because it has intrinsic curvature that no bending can remove. That single geometric fact - Gauss’s theorema egregium - is why all map distortion exists.

Answer: D

Correct answer: Mercator

Mercator’s projection has the property that a rhumb line, a course of constant compass bearing, is a straight line on the chart. A navigator could therefore draw a line between two ports, measure its angle against a meridian, and steer that bearing throughout. It is not the shortest route, but before electronic navigation the ease of steering it usually outweighed the extra distance.