# 21.1 Basic Definitions

**The Distance Formula • The Slope of a Line • Inclination • Parallel Lines • Perpendicular Lines**

As we have noted, analytic geometry deals with the relationship between an algebraic equation and the geometric curve it represents. In this section, we develop certain basic concepts that will be needed for future use in establishing the proper relationships between an equation and a curve.

# THE DISTANCE FORMULA

The first of these concepts involves the distance between any two points in the coordinate plane. If these points lie on a line parallel to the `x`-axis, the distance from the first point $({x}_{1}\hspace{0.17em},\hspace{0.17em}\text{}y)$ to the second point $({x}_{2}\hspace{0.17em},\hspace{0.17em}\text{}y)$ is $|\hspace{0.17em}{x}_{2}\hspace{0.17em}-\hspace{0.17em}{x}_{1}|\hspace{0.17em}\hspace{0.17em}.\hspace{0.17em}$ The absolute value is used because we are interested only in the magnitude ...

Get *Basic Technical Mathematics, 11th Edition* now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.