Understanding Segments in Mathematics: Length, Midpoint, Collinear Points, and Rays

Segment

Segment in mathematics refers to a part of a line that is bounded by two distinct endpoints

Segment in mathematics refers to a part of a line that is bounded by two distinct endpoints. It is a one-dimensional object that has a measurable length. A segment is represented by drawing a line between the two endpoints and is usually denoted using the symbol AB, where A and B are the endpoints.

Here are a few key concepts related to segments:

1. Length: The length of a segment is the distance between its two endpoints. It can be measured using a ruler or by applying the distance formula based on the coordinates of the endpoints.
– For example, if the endpoints A and B have coordinates (x1, y1) and (x2, y2) respectively, then the length of the segment AB is given by the formula: √[(x2 – x1)^2 + (y2 – y1)^2].

2. Midpoint: The midpoint of a segment is the point that divides the segment into two equal halves. It is equidistant from both endpoints and is denoted by the letter M.
– The coordinates of the midpoint can be found by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints.

3. Collinear points: Three or more points are said to be collinear if they lie on the same line. In the context of a segment, the two endpoints and all the points on the line that lie between them are collinear.

4. Ray: A ray is a part of a line that has one endpoint and extends infinitely in the other direction. A ray can be defined by specifying the starting point and a direction in which it continues.
– A ray can be denoted using two letters, with the first letter representing the endpoint and the second letter indicating the direction it travels.

It is important to note the difference between a segment and a line. While a segment has finite length and is bounded by two endpoints, a line extends infinitely in both directions with no endpoints.

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