[list][*]extend our understanding of Cartesian coordinates,[/*][*]re-introduce notations for points, lines, and planes,[/*][*]extend our distance formula,[/*][*]extend formulas for lines, planes, and some circular 3D surfaces.[/*][/list]
We begin by "assigning" a point's location in by measuring in two dimensions (directions): [math]x[/math] and [math]y[/math].[br][br]We can describe these directions into quadrants (1, 2, 3, and 4) by categorizing the numbers of each axis into [i]negative[/i], 0, and [i]positive[/i] numbers.
[list][*]What quadrants are possible for a point with coordinate [math]x=3[/math]?[/*][/list]
Next we apply these ideas to a universe in which we've added one new set of axes.[br](Or, in which we've added a new coordinate.)[br][br]We "assigning" a point's location in by measuring in [i]three[/i] dimensions (directions): [math]x[/math], [math]y[/math] and [math]z[/math].[br][br]We can describe these directions into [s]quadrants[/s] octants (1, 2, 3, 4, 5, 6, 7, and 8) by again categorizing the numbers of each axis into [i]negative[/i], 0, and [i]positive[/i] numbers.