I would love to have answer to this issue I have been trying to resolve.
In a 2km square kilometer (2km2) with midpoint at 1km, the Longitude and Latitude of the midpoint are known and the origins of the X and Y coordinates of the square start at zero (0, 0) to positive X and Y values (with boundary at 2km respectively).
(1) How would one determine the Longitudes and Longitudes of the four boundary points [at (0, 0), (0, 2), (2, 0), (2, 2)].
If there are about 100 places (or points) within this square with known Latitudes and Longitudes, how would one determine the respective x, y values (in km) of these 100 points with respect to the origins at zero
Essentially you're mapping one Cartesian coordinate system onto another. Here's how to transform coordinate systems linearly and with rotation in case your square doesn't align with north-south and west-east already (link below). We're simplifying by assuming latitude and longitude are a Cartesian grid, which I feel is justified for practical purposes over a 4 km2 region since it's so small relative to the Earth's 510 million km2. But if you'd like to get fancier, latitude and longitude are a spherical coordinate system of two angles with the radius of the Earth adjusted for altitude. You can use standard formulas to convert it to an XYZ frame of reference (second link below). Hope this helps, Ikechukwu. ~ Kevin
Transform a Cartesian coordinate system to another:
https://www.accessengineeringlibrary.com/content/book/9780071761123/back-matter/appendix3
Transform Spherical coordinates to Rectangular coordinates:
https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(OpenStax)/12%3A_Vectors_in_Space/12.7%3A_Cylindrical_and_Spherical_Coordinates
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