The scale factor in a transverse Mercator projection varies with which factor?

The scale factor in a transverse Mercator projection is primarily affected by latitude. This projection is designed to minimize distortion along the central meridian, where the scale factor is 1. However, as you move away from the central meridian, distortion increases, affecting the scale factor.

Specifically, the scale factor is related to the latitude because the curvature of the Earth affects how distances are represented on the flat surface of the map. At higher latitudes, the distortion increases more significantly than at lower latitudes. Therefore, while longitude can also play a role in the context of the projection overall, the primary influence on the variation of the scale factor is latitude, making that the correct focus for this question.

In summary, the scale factor in a transverse Mercator projection varies with latitude due to the nature of the projection's design and its relationship with the Earth's spherical shape.