Which projection maps arc lengths along a chosen meridian into rectangular coordinates on a plane?

Which projection maps arc lengths along a chosen meridian into rectangular coordinates on a plane?

• A. Cylindrical Projection
• B. Azimuthal Projection
• C. Conical Projection
• D. Cassini Projection

Answer: (D)

The key idea is preserving distances along a chosen line of longitude when you project to a plane. In the Cassini projection, the scale along a central meridian is kept exact, so moving along that meridian on the globe translates directly into a proportional, linear movement on the map. This makes the meridional arc length correspond to a straight, vertical (or defined) coordinate on the plane, giving you a rectangular coordinate system where distance along the meridian is represented faithfully. Other projections don’t keep meridional distances exact along a chosen meridian. Cylindrical projections typically spread or compress distances based on latitude, azimuthal projections optimize directions from a point, and conical projections center on a cone and distort distances away from the reference line. So for the specific aim of turning arc lengths along a meridian into a linear plane coordinate, the Cassini projection best fits.

The key idea is preserving distances along a chosen line of longitude when you project to a plane. In the Cassini projection, the scale along a central meridian is kept exact, so moving along that meridian on the globe translates directly into a proportional, linear movement on the map. This makes the meridional arc length correspond to a straight, vertical (or defined) coordinate on the plane, giving you a rectangular coordinate system where distance along the meridian is represented faithfully.

Other projections don’t keep meridional distances exact along a chosen meridian. Cylindrical projections typically spread or compress distances based on latitude, azimuthal projections optimize directions from a point, and conical projections center on a cone and distort distances away from the reference line. So for the specific aim of turning arc lengths along a meridian into a linear plane coordinate, the Cassini projection best fits.