2-Dimensional Cartesian Coordinate System

∟2-Dimensional Cartesian Coordinate System

This section provides an introduction of 2-dimensional Cartesian coordinate systems, which uses perpendicular projections on 2 perpendicular axes to describe any locations in the frame of reference.

When describing an object that is moving along non-straight line, we need to use 2-dimensional or 3-dimensional frame of references and coordinate systems.

For example, the trajectory of a flying golf ball is not a straight line, but it can described with a 2-dimensional frame of reference and an associated coordinate system.

First, let's define a 2-dimensional frame of reference as a vertical rectangle:

The first edge runs from the golf ball stand to target hole.
The second edge runs from the golf ball stand straight up to the sky for 10 meters.
The third edge runs from the target hole straight up to the sky for 10 meters.
The last edge connects the end point of the second edge and the first edge.

Next, let's create a simple coordinate system:

Set a 2-dimensional Cartesian coordinate system on the frame of reference.
Set the origin of the Cartesian coordinate system at the golf ball stand.
Set the x-axis along the first edge of the frame of reference. Scale the x-axis with 1 meter per unit.
Set the y-axis along the second edge of the frame of reference. Scale the x-axis with 1 meter per unit.

Now we are can describe any location of the golf ball while it's flying in the air as a pair of coordinate numbers by reading scales of its perpendicular projections on the x-axis and the y-axis.