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Ordered Triples


An ordered triple is a list of 3 elements written in a certain order. As with ordered pairs, order is important.

For example, the numbers 1, 2 and 3 can form 6 ordered triples: (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1).

Cartesian Coordinate System in 3-D

An ordered triple such as (x,y,z) can be represented by a point in a coordinate system with three axes, the Cartesian Coordinate System in 3-D. To draw the three axes, first draw a 2-D Cartesian coordinate system and label the axes y and z. Next, we draw a third axes that it is perpendicular to the other two and label the axes x (imagine that the x-axis is pointing directly at you).

The intersection of the three axes is called the origin. It represents the triple (0,0,0) and will be denoted by 0.

The following example illustrates how to represent an ordered triple as a point on this 3-dimensional grid.

Example 3.

To locate the point represented by (2,3,3):

First draw a line parallel to the y-axis through x =2.

Next draw a line parallel to the x-axis through y =3. The two lines intersect at a point B.

Finally, draw a line of length 3 parallel to the z-axis through B, the intersection of the first two lines. The point (2,3,3) is located at the top of this line.


Exercise illustrated visually on grid.

More Exercises (opens in new window)


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