Match List I with List II and select the correct answer using the code given below:
List I (Projection) - List - II (Property)
(a) Azimuthal - (i) Correct Shape
(b) Orthomorphic - (ii) True Bearing
(c) Homolographic - (iii) Equal Area
(d) Mercator - (iv) Rhumb Line
Code :

Question

Match List I with List II and select the correct answer using the code given below: 
List I (Projection) - List - II (Property)
(a) Azimuthal - (i) Correct Shape
(b) Orthomorphic - (ii) True Bearing
(c) Homolographic - (iii) Equal Area
(d) Mercator - (iv) Rhumb Line
Code :

Accepted Answer

Here's a detailed explanation justifying why Option 3 is the correct answer and why the other options are incorrect, based on the given information:

**Justification for Option 3 being correct:**

Option 3 states the following matches:

*   **(a) Azimuthal - (ii) True Bearing:** Azimuthal projections are specifically designed to preserve directions from a central point. This means that bearings (directions relative to North) are accurately represented. Therefore, Azimuthal projections have the property of showing *True Bearing*.

*   **(b) Orthomorphic - (i) Correct Shape:** Orthomorphic projections (also known as conformal projections) prioritize preserving the shape of small areas. While they distort area, they maintain the angles between lines, ensuring that shapes are locally accurate. Hence, Orthomorphic projections have the property of *Correct Shape*.

*   **(c) Homolographic - (iii) Equal Area:** Homolographic projections are designed to preserve area. This means that the relative sizes of regions on the map are accurately represented, even if their shapes are distorted. Therefore, Homolographic projections have the property of *Equal Area*.

*   **(d) Mercator - (iv) Rhumb Line:** The Mercator projection is unique in that straight lines on the map represent lines of constant bearing (rhumb lines or loxodromes). This makes it particularly useful for navigation, as a navigator can draw a straight line between two points on the map and follow that bearing. Thus, Mercator projections have the property of *Rhumb Line*.

**Explanation of why other options are incorrect:**

*   **Option 1: (a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)**
    *   (a)-(iii): Azimuthal projections do *not* primarily preserve area (Equal Area). They preserve direction from a central point.
    *   (b)-(ii): Orthomorphic projections do *not* primarily preserve true bearing. They preserve shape.
    *   (c)-(i): Homolographic projections do *not* primarily preserve shape (Correct Shape). They preserve area.

*   **Option 2: (a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)**
    *   (a)-(iii): Azimuthal projections do *not* primarily preserve area (Equal Area). They preserve direction from a central point.
    *   (c)-(iv): Homolographic projections do *not* primarily show rhumb lines. They preserve area.
    *   (d)-(ii): Mercator projections do *not* primarily show true bearing from all points. They show rhumb lines as straight lines.

*   **Option 4: (a)-(ii), (b)-(iii), (c)-(i), (d)-(iv)**
    *   (b)-(iii): Orthomorphic projections do *not* primarily preserve area (Equal Area). They preserve shape.
    *   (c)-(i): Homolographic projections do *not* primarily preserve shape (Correct Shape). They preserve area.

In summary, Option 3 correctly matches each projection type with its primary property, while the other options contain incorrect pairings. Therefore, Option 3 is the correct answer.