![]() The word plane is written with the letter so as not to be confused with a point (Figure 4 ). So, most of the lines that we experience in our everyday reality are actually line segments when we think of it from a pure geometrical point of view. The figure (shown in 2D for simplicity) shows that if P is a point on the line then langle x,y rangle P + tvnonumber for some number (t). But why we call it a segment is that it actually has a starting and a stopping point. Our goal is to come up with the equation of a line given a vector v parallel to the line and a point (a,b,c) on the line. For lack of a better word, a straight line. A single capital letter is used to denote a plane. A line segment is something just like that. It is usually represented in drawings by a four‐sided figure. A plane has infinite length, infinite width, and zero height (or thickness). In Figure 3 , points M, A, and N are collinear, and points T, I, and C are noncollinear.įigure 3 Three collinear points and three noncollinear points.Ī plane may be considered as an infinite set of points forming a connected flat surface extending infinitely far in all directions. If there is no line on which all of the points lie, then they are noncollinear points. Points that lie on the same line are called collinear points. A line may also be named by one small letter (Figure 2). The symbol ↔ written on top of two letters is used to denote that line. ![]() A line has infinite length, zero width, and zero height. It extends infinitely far in two opposite directions. Figure 1 illustrates point C, point M, and point Q.Ī line (straight line) can be thought of as a connected set of infinitely many points. A point represents position only it has zero size (that is, zero length, zero width, and zero height). Point, line, and plane, together with set, are the undefined terms that provide the starting place for geometry. It is represented by a dot and named by a capital letter. Although these terms are not formally defined, a brief intuitive discussion is needed.Ī point is the most fundamental object in geometry. A line is a connected set of points that extends infinitely in two directions. These terms will be used in defining other terms. Key Points A point is a location in space. Because that meaning is accepted without definition, we refer to these words as undefined terms. This process must eventually terminate at some stage, the definition must use a word whose meaning is accepted as intuitively clear. When we define words, we ordinarily use simpler words, and these simpler words are in turn defined using yet simpler words. Point, line, and plane, together with set, are the undefined terms that provide the starting place for geometry. Summary of Coordinate Geometry Formulas A plane, a plane is a flat surface made up of an infinite number of points.Slopes: Parallel and Perpendicular Lines. ![]()
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