Welcome to 3D coordinate systems! A 3D coordinate system allows us to locate any point in three-dimensional space. It consists of three perpendicular axes - X, Y, and Z - that intersect at a central point called the origin. Each point in 3D space can be described using three coordinates that represent its position along each axis.
Let's examine the three axes in detail. The X-axis runs horizontally from left to right, typically colored red. The Y-axis extends from front to back, showing depth, and is usually green. The Z-axis points vertically upward, commonly shown in blue. These three axes are mutually perpendicular, meaning each axis forms a 90-degree angle with the other two.
Now let's learn how to write coordinates in 3D space. Every point is represented by an ordered triplet written as (x, y, z). The first number is the x-coordinate showing position along the X-axis, the second is the y-coordinate for the Y-axis, and the third is the z-coordinate for the Z-axis from the origin.
In 3D coordinate systems, space is divided into eight regions called octants, similar to how 2D space has four quadrants. Each octant is characterized by the combination of positive and negative values for x, y, and z coordinates. The first octant contains all positive coordinates, while the other seven octants have different combinations of positive and negative values.