How to Put Points on a 3D Coordinate Plane

Coordinates are the basics for any three-dimensional construction.

The coordinate planes, created by René Descartes, are the basis for analytic geometry. Any point in space is represented by a three-element coordinate. Each element on the coordinate set represents a position on each axis. It is difficult to work with a three-dimensional (3D) coordinate system, since its representation on paper might conduct to misleading conclusions. Quite often is easier to work on the planes that make up the 3D system (XY, YZ and ZX). Locating and placing points on a 3D plane is a good exercise to practice these skills.

Instructions

1. Write down the coordinates for the points you wish to place on the 3D coordinate axis. Points have three numbers that determine its coordinates. For example, consider point A (+1, -3, +5).

2. Locate the X axis and place a mark at the first coordinate point. Draw a line through the first point. The line must be located on the YZ plane and perpendicular to the X axis.

   From the example, A (+1, -3, +5), the line on the YZ axis must pass over "+1."

3. Place a mark on the Y axis that matches the second coordinate. Draw a line on the XZ plane, perpendicular to the Y axis. In the example, A (+1, -3, +5), the line on XZ its perpendicular to "-3" on the Y axis.

4. Locate and mark the third coordinate on the Z axis. Draw a line on the XY plane, perpendicular to the Z axis. In the example A (+1, -3, +5), the line on the XY plane will pass through "+5" on the Z axis.

5. Extends the three perpendicular lines until they all cut in the same point. The intersection of the three lines will be the location of the 3D point.

Tips & Warnings

• When extending the lines (Step 5), be sure to extend them both directions.

References

• University of Tennessee: Physics Department; 3D Coordinate Systems: Cartesian Coordinates