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Line Segment

Line Segment
Segment

All points between two given points (including the given points themselves).

 

Example:    line segment Line segment AB with endpoints labeled A and B connected by a straight horizontal line.

Line segment AB with endpoints labeled A on the left and B on the right, connected by a straight line.

Worked Example

Problem: Find the length of the line segment from point A(1, 2) to point B(4, 6).
Step 1: Identify the coordinates of the two endpoints.
A=(1,2),B=(4,6)A = (1, 2), \quad B = (4, 6)
Step 2: Apply the distance formula to find the length of the segment.
AB‾=(4−1)2+(6−2)2=9+16=25\overline{AB} = \sqrt{(4-1)^2 + (6-2)^2} = \sqrt{9 + 16} = \sqrt{25}
Step 3: Simplify to get the length.
AB‾=5\overline{AB} = 5
Answer: The line segment from A to B has a length of 5 units.

Why It Matters

Line segments are the building blocks of nearly every geometric figure. Triangles, rectangles, and polygons are all formed by connecting line segments end to end. Measuring and comparing line segments is also fundamental to coordinate geometry, construction, and real-world applications like architecture and engineering.

Common Mistakes

Mistake: Confusing a line segment with a line or a ray.
Correction: A line extends infinitely in both directions and has no endpoints. A ray has one endpoint and extends infinitely in one direction. A line segment has exactly two endpoints and a finite, measurable length. In notation, AB‾\overline{AB} denotes a segment, while AB↔\overleftrightarrow{AB} denotes a line and AB→\overrightarrow{AB} denotes a ray.

Related Terms

  • Point — Endpoints that define a line segment
  • Between — Describes points lying on a segment
  • Line — Extends infinitely, unlike a segment
  • Ray — Has one endpoint, extends one direction
  • Midpoint — The point exactly halfway along a segment