To determine the origin with two coordinates, one must first identify the common point between the two sets of coordinates. This common point represents the origin, which is the starting point from which all other distances and directions are measured. For example, if you have two coordinates (X1, Y1) and (X2, Y2), the origin can be found by calculating the midpoint between these two points. The midpoint coordinates (Xm, Ym) are calculated as follows:

Xm = (X1 + X2) / 2

Ym = (Y1 + Y2) / 2

This method assumes that the coordinates are in a two-dimensional plane. If the coordinates are in a three-dimensional space, the origin would be the point where the three coordinates intersect.

The reason this method works is based on the principles of geometry and the concept of the midpoint. The midpoint of a line segment is equidistant from both endpoints, making it the origin for the segment. This concept is fundamental in various fields, such as navigation, cartography, and computer graphics, where determining the origin is crucial for accurate representation and calculations.

According to the U.S. National Geospatial-Intelligence Agency (NGA), accurate determination of the origin is essential for mapping and geospatial analysis. The NGA states that "the origin of a coordinate system is the point from which all other coordinates are measured. It is the zero point of the coordinate system." This highlights the importance of the origin in various applications, including military, civilian, and scientific endeavors.

In conclusion, determining the origin with two coordinates involves finding the midpoint between the two points. This method is grounded in geometric principles and is widely used in various fields due to its accuracy and simplicity. The NGA's emphasis on the origin's importance further underscores its significance in geospatial applications.