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Coordinate Geometry is also Analytic Geometry, founded by Rene Descartes.
Coordinate geometry is mainly used in computers for computer graphics software. Coordinate geometry is two-dimensional, and includes shapes such as lines and polygons.
If by sperical triangle you mean a triangle on the surface of a sphere, you will need 3 dimensional coordinate geometry. Whether you use polar coordinates or linear coordinates will depend on what you want to "solve".
you count the number of boxes IN the shape.
by using coordinate geometry you can find the position of a place in earth by using the pictures taken by satellites.