A geometrical object that is straight, infinitely long and infinitely thin.
Try this Drag the orange dot at P or Q and see how the line PQ behaves.

In the figure above, the line PQ passes through the points P and Q, and goes off in both directions forever, and is perfectly straight. A line, strictly speaking, has no ends.

A line is one-dimensional. It has zero width. If you draw a line with a pencil, examination with a microscope would show that the pencil mark has a measurable width. The pencil line is just a way to illustrate the idea on paper. In geometry however, a line has no width.

A straight line is the shortest distance between any two points on a plane.

Drawing a line

You can draw a line that just goes off the edges of the page, as in the figure above. More commonly it is shown as a line with an arrow head on each end as shown below. The arrow heads mean that the line goes off to infinity in both directions.
A line, passing through two points, with an arrow head at each end indicating its continuation to infinity

Lines are commonly named in two ways:

  1. By any two points on the line. In the figure above, the line would be called JK because it passes through the two points J and K. Recall that points are usually labelled with single upper-case (capital) letters. There is a symbol for this which looks like
    . This is read as "line JK".  The two arrow heads indicate that this is a line which passes through J and K but goes on forever in both directions.
  2. By a single letter.
    The line above could also be called simply "y". By convention, this is usually a single lower case (small) letter. This method is sometimes used when the line does not have two points on it to define it.

Coordinate Geometry

In another branch of mathematics called coordinate geometry, the points that define a line are located on the plane using their coordinates - two numbers that show where the point is positioned.
For more on this, see Definition of a line (Coordinate Geometry).

If a line is not straight, we usually refer to it as a curve or arc. In plane geometry the word 'line' is usually taken to mean a straight line.

If a set of points are lined up in such a way that a line can be drawn through all of them, the points are said to be collinear. See Collinear definition.

Other line topics


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