Question

Which of the following is/are preserved in the Mercator projection?

• A. Shape
• B. True direction
• C. Equal area
• D. Shape only along the standard parallel

Hint:

The Mercator projection is conformal, think about what conformality guarantees about local angles/shape everywhere on the map, and why rhumb lines plot as straight lines, then check whether area is exaggerated at high latitudes.

Answer 1

The Correct Option is A, B

Step 1: Recall what type of projection the Mercator is.
The Mercator projection is a cylindrical projection constructed so that it is conformal, meaning that at every point on the map the angles between any two intersecting lines on the Earth's surface are reproduced exactly on the map. A direct consequence of conformality is that the scale at any single point is the same in every direction from that point, so small shapes (for example the outline of a small island or a small country) are rendered on the map without angular distortion, that is, their local shape is preserved everywhere on the map, not only along one particular line.

Step 2: Explain why true direction is preserved.
Because the projection is conformal and, in addition, meridians and parallels are drawn as a rectangular grid of straight, mutually perpendicular lines, a line of constant compass bearing on the Earth (a rhumb line or loxodrome) is drawn as a single straight line on the Mercator map. This means a navigator can plot a straight line course on the map and read off a true, constant compass direction, which is exactly why the Mercator projection was originally developed for marine navigation and is described as preserving true direction.

Step 3: Explain why equal area is not preserved.
To keep the map conformal, the Mercator projection must stretch the east-west scale and the north-south scale by the same growing factor as latitude increases, this factor grows as \(\sec(\phi)\) at latitude \(\phi\), becoming infinite at the poles. As a result the area shown on the map for a fixed size region on the ground grows rapidly with latitude, for example Greenland appears comparable in size to Africa on a Mercator map even though Africa's true area is about fourteen times larger, so the projection clearly does not preserve area, which rules out option (C).

Step 4: Explain why option (D) is a wrong restriction.
Option (D) claims shape is preserved only along the standard parallel, but that description actually applies to scale, not shape, the true, undistorted linear scale of the Mercator projection occurs along the standard parallel (or the equator if there is no separate standard parallel), while conformality, and hence the preservation of local shape and angles, holds at every point of the map, not just along that one parallel. So option (D) misapplies the "true only along the standard parallel" property, which belongs to scale, to shape, making it incorrect.

Step 5: Conclusion.
The Mercator projection, being conformal, preserves local shape everywhere and preserves true direction through straight rhumb lines, but does not preserve area, so the correct options are shape and true direction.

\[ \boxed{\text{Shape and True direction}} \]