Line segment

Introduction to Line Segments

  • A line segment is a part of a line that is bounded by two distinct end points and contains every point on the line between its endpoints.
  • Unlike a line, a line segment starts at one point and ends at another; it doesn’t continue indefinitely in either direction.
  • The length of a line segment is the distance between its two end points.

Characteristics of Line Segments

  • Every line segment is both closed (includes its endpoints) and bounded (the endpoints serve as boundaries).
  • Two line segments are congruent if they have the same length, regardless of their position and orientation.
  • Midpoint is the point that divides a line segment equally into two segments. If the end points of the line segment are (x1, y1) and (x2, y2), then the midpoint is given by ( (x1+x2) / 2, (y1+y2) / 2).

Problems Involving Line Segments

  • Problems involving line segments often include calculating the length of a line segment or finding the midpoint.
  • To calculate the length of a line segment, we can use the distance formula if the coordinates of the endpoints are known. The formula is sqrt[ (x2-x1)² + (y2-y1)² ].
  • Pythagorean theorem is used often in line segment problems where you have a right-angled triangle.

Examples of Line Segments

  • Line segments are fundamental components in many geometrical shapes such as squares, rectangles, triangles and more complex polygons.
  • They are also helpful in defining and visualising vectors, which have both direction and magnitude.
  • In statistics, line segments are used to create graphs and charts like the histogram, where each line segment represents a specific data set.

Practical Applications of Line Segments

  • Being skilled with line segments is important for a variety of fields beyond mathematics, such as art, architecture, physics, and graphic design.
  • In physics, Line segments are used to represent vectors such as forces and velocities.
  • They are also essential in computer graphics for rendering shapes on a digital screen.

Extra Notes

  • It’s important to remember that a line segment has a fixed length, unlike a line or ray.
  • Make sure to practise problem-solving involving line segments, for example calculating distances or midpoints.
  • Always remember that the length of a line segment is the numerical difference of the coordinates of its endpoints in a one-dimensional space.