# Three-Dimensional Coordinate Geometry

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## Abstract

Before we lead on to a study of the graphical display of objects in three-dimensional space, we first have to come to terms with the three-dimensional Cartesian coordinate geometry. As in two-dimensional space, we arbitrarily fix a point in the space, named the *coordinate origin* (or *origin* for short). We then imagine three mutually perpendicular lines through this point, each line going off to infinity in both directions. These are the *x-axis,* the *y-axis* and the *z-axis.* Each axis is thought to have a positive and a negative half, both starting at the origin; that is, distances measured from the origin along the axis are positive on one side and negative on the other. We may think of the *x*-axis and *y*-axis in the same way as we did for two-dimensional space, both lying on the page of this book say, the positive *x*-axis ‘horizontal’ and to the right of the origin, and the positive *y*-axis ‘vertical’ and above the origin. This just leaves the position of the *z*-axis: it has to be perpendicular to the page (since it is perpendicular to both the *x*-axis and the *y*-axis). The positive *z*-axis can be into the page (the so-called *left-handed triad* of axes) or out of the page (the *right-handed triad*). *In this book we always use the left-handed triad notation.* What we say in the remainder of the book, using left-handed axes, has its equivalent in the right-handed system — it does not matter which notation you finally decide to use *as long as you are consistent.*

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