The derivate of coordinates

Grade 10
Mathematics

The Derivate of Coordinates

To begin I must first introduce what coordinates are. Coordinates are the ordered numbers used to represent the location of a point in a plane or space. Then comes the Coordinate system which is a plane or space were the origin (“0”) and the axes (x,y) are placed so that coordinates can be measured. X is a horizontal line (abscissa) and Yis a vertical line (ordinate) that is parallel to X, the intersection of the axes (x,y) leave four regions that are called quadrants that are represented in roman numbers; This numbers start from the upper left region (I, II, III, IV) and keeps on going counter clock wise.

A set of coordinates is shown like this: “(4, 2)” four being the “x” or horizontal position and two being “y” in thevertical position. It sometimes happens that one of the coordinates is negative, in which case the point position is different. If the abscissa (“x” coordinate) is negative, then the point would be on the left side of the ordinate (“y” coordinate). If the case is that the ordinate is negative then the point would go bellow the abscissa line. It can ALSO be the case that both coordinates are negative.As we can see the coordinate system starts from coordinates, and from this simple concepts many variations appear, all using the same principles.

Now, there are many topics that use coordinates; we might not see the coordinates pair such as “(2, 6)” in the same way like in the coordinate system, but the plane or space can be seen, in other words the “axes”. The coordinate system is used inmost of the branches of mathematics, from geometry up to algebra; coordinates are almost a universal base too many subjects since the same axes are widely used, this can be seen by the fact that it is used in Physics. Some of the most common subjects that use coordinate systems are the Polar coordinate system, Parallel coordinates, and Analytical Geometry, but by far the one that is more common andpopular is the Cartesian coordinate system.

The Cartesian coordinate system can be used in dimensions. The Two-dimensional (2D) coordinate system which it basically is the coordinate system that I’ve explained above, it often has the letter P to represent point. It is very common to find equations made out of the Cartesian plane (which are the axis and the quadrants) in order to find specificinformation. The Three-dimensional (3D) coordinate system provides the three physical dimensions of space, in here another axis is added (z) in order to create 3D shapes; by consequence eight subdivisions are created which are known as octants, like the quadrants in the 2D coordinate system.[1]

In truth, the Coordinate system is much more complex and has a lot more branches and subdivisionsthat it would take a while and a lot of space to explain all of them, but now that the basics have been covered I’ll be moving on into the topic that captures my interest the most and that I’ll be getting into more detail which is Coordinates and Geography. Geographic coordinates and Spherical coordinate system are used in geography to map the world.

The Spherical coordinate system is a systemused to represent geometric figures in 3D with the help of three coordinates.
Geographic coordinates allows people to find any location in Earth by three coordinates in a Spherical coordinate system (same basics of the 3D coordinate system) that is aligned with the axis of the Earth.

Latitude and Longitude are the first and second dimensions of the Geographic coordinates. This concept beganwith the Babylonians and was extended by the Greek thinker Ptolemy that in his work called Geographia explained the method he used and how he used it, even if some of his methods were not exact, they were the beginning of Latitude and Longitude as we know it.

Any location in earth can be found with two numbers, the latitude and longitude that receive the names of parallels and meridians....