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.