AutoCAD uses the Cartesian coordinate system as a basis to layout its vectors. Each coordinate is the distance of a point on the x-, y-, or z-axis from the origin.
In 2D settings, it uses the (x , y) format.
In 3D settings, it uses the (x, y, z) format.
For example, you do the LINE command and place it at (0, 0), that coordinate will be the start of the line segment. The next point clicked, for example (2, 3) is going to be the end of that line segment.
If you use the "@" notation when placing vectors, you have a distance compared to what the previous point was instead of compared to the origin.
For example, if you added another line segment onto the previous line that went from (0, 0) to (2, 3), you might want the line to go 1 unit up and 1 unit right compared to the previous endpoint (2, 3). If this is so, you can do "@1, 1" to make the line segment go 1 up and 1 right from the previous point.
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You do not have to. You could use polar coordinates, if you prefer.
( x y z )
Yes! By expanding the system to 3D!
Possibly because the first time that pupils are introduced to the name and concept it is has only two dimensions. These are usually represented as horizontal (x) and vertical (y) coordinates. Actually, many children meet the concept - in its 1-dimensional form - as the number line. It is not called a Cartesian coordinate system then, and they make only simple use of it. The Cartesian coordinate system is normally extended to 3-dimensional space in high school coordinate geometry when it is obviously not called a plane, and to multi-dimensional hyperspaces in advanced mathematics or physics.
The Cartesian coordinate system allows a geometric curve to be described in algebraic terms. This then allows the use of algebraic tools including differentiation and integration to be used to solve geometric problems such as the turning points of curves, their volumes of rotation and so on. It also enables geometric methods to be applied to solving algebraic problems.