Lines

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It has one dimension, length. Points that are on the same line are called collinear points. A part of a line that has defined endpoints is called a line segment.

A line segment as the segment between A and B above is written as:. A plane extends infinitely in two dimensions. It has no thickness. An example of a plane is a coordinate plane. A plane is named by three points in the plane that are not on the same line. Here below we see the plane ABC.

A space extends infinitely in all directions and is a set of all points in three dimensions. You can think of a space as the inside of a box. A line is defined by two points and is written as shown below with an arrowhead. Video lesson Plot a pint, a line, a line segment and an angle in a coordinate plane. Euclid defined a line as a "breadthless length," and a straight line as a line that "lies evenly with the points on itself" Kline , Dunham Consider first lines in a two-dimensional plane.

Books & Journals

Two lines lying in the same plane that do not intersect one another are said to be parallel lines. Two lines lying in different planes that do not intersect one another are said to be skew lines. The line with x -intercept and y -intercept is given by the intercept form. It is not uncommon for lines in intercept form to be rewritten in what's known as standard form :.

The line through with slope is given by the point-slope form. The line with -intercept and slope is given by the slope-intercept form. The line through and is given by the two-point form. A line in two dimensions can also be represented as a vector. The vector along the line.

Horizontal & vertical lines

Similarly, vectors of the form. The line joining points with trilinear coordinates and is the set of point satisfying. The line through in the direction and the line through in direction intersect iff. The line through a point parallel to. In three-dimensional space , the line passing through the point and parallel to the nonzero vector has parametric equations.

Similarly, the line in three dimensions passing through and has parametric vector equation. Portions of this entry contributed by Christopher Stover. Casey, J. Dunham, W.

NIST: Atomic Spectra Database Lines Form

New York: Wiley, p. Harary, F. Graph Theory.

Reading, MA: Addison-Wesley, Jurgensen, R. Modern Geometry: Structure and Method. Boston, MA: Houghton-Mifflin, p.


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