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Line
A geometrical object that is (usually) straight, infinitely long and infinitely thin.
Try this Adjust the line segment below by dragging an orange dot at P or Q and see how the line PQ behaves.
(If there is no image below, see support page.)

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

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

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

Naming of lines

Lines are commonly named in two ways:
  1. By points on the line.
    In the figure above, the line would be called PQ because it passes through the two points P and Q. Recall that points are usually labelled with single upper-case (capital) letters. There is a symbol for this which looks like
    PQ
    . This is read as "line PQ".  The two arrow heads indicate that this is a line which passes through P and Q 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 used when the line does not pass through two points.

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).

Definition note

In solid geometry, a line may actually be curved. For example a line may be drawn on the surface of a sphere. In plane geometry, we define it as totally straight in all dimensions.

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

Other line topics

(C) 2009 Copyright John Page