Which of the following is/are preserved in the Mercator projection?
Show 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.
Step 1: Classify the Mercator projection by its preserved property. Map projections are broadly grouped by which single Earth-to-map property they hold exactly true: conformal projections preserve local angles and shape, equal-area (equivalent) projections preserve area, and equidistant projections preserve distance along certain lines. The Mercator projection belongs to the conformal group.
Step 2: Derive the consequence of conformality for shape. A conformal projection is defined by having the same scale factor $h$ in every direction at any given point, that is $h_{meridian} = h_{parallel}$ at each point, even though $h$ itself changes from point to point (increasing with latitude on the Mercator). Because the stretching is identical in all directions at a point, small figures keep their correct angles and proportions locally, this is exactly what "shape is preserved" means for a conformal map, and it is true at every point on the map, not restricted to a single parallel.
Step 3: Derive the consequence for direction. On the Mercator grid, meridians are evenly spaced parallel vertical lines and parallels are horizontal lines perpendicular to them. A rhumb line, a path of constant true compass bearing $\theta$ on the sphere, crosses every meridian at the same angle $\theta$. Since the Mercator grid keeps meridians parallel and straight, a curve crossing them all at a constant angle plots as a straight line on the map, at that same angle $\theta$. This straight-line, constant-bearing property is what is meant by the projection preserving true direction.
Step 4: Show area is not preserved. The point scale factor on the Mercator projection is $h(\phi) = \sec(\phi)$, where $\phi$ is latitude, and since area scales as $h^2 = \sec^2(\phi)$, the apparent area of a fixed ground region grows without bound as $\phi \to 90^\circ$. This strong area exaggeration at high latitudes directly contradicts option (C), equal area is not a property of this projection.
Step 5: Show why option (D)'s wording is wrong. It is the scale factor $h$ that equals exactly 1, the true, undistorted value, only along the standard parallel (or the equator), while conformality itself, and therefore shape preservation, holds everywhere on the map since $h$ is equal in both directions at every point regardless of its magnitude. So restricting "shape preserved" to just the standard parallel, as option (D) does, incorrectly borrows the scale property and misapplies it to shape.
Step 6: Conclusion. Being a conformal cylindrical projection, the Mercator projection preserves local shape everywhere and preserves true compass direction along straight rhumb lines, so shape and true direction are the two preserved properties.
