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Identify points, lines, rays, and segments

A point represents an exact location; a line extends infinitely in both directions, a ray has one endpoint and extends infinitely in one direction, and a segment has two endpoints and a finite extent. Diagrams and standard notation distinguish endpoints from arrowheads, while recognizing that a drawing of a line or ray is only a representation of an unbounded object; the focus is on these basic relationships rather than coordinate equations or formal axiomatic treatment.

Detailed Explanation: Identify points, lines, rays, and segments

A figure’s end markings tell you what it represents:

  • A point is an exact location, shown by a dot. It is named with one capital letter, such as PP.
  • A line extends forever in both directions, so it has arrowheads on both ends. It is named with two points, such as QR\overleftrightarrow{QR}.
  • A ray has one endpoint and extends forever in one direction. It has one dot and one arrowhead. Name the endpoint first, such as ST\overrightarrow{ST}.
  • A segment has two endpoints and a finite length. It has dots on both ends and no arrowheads. It is named with two points, such as UV\overline{UV}.

Worked example

Identify each figure.

1.        • P

2.   ←────•────────•────→
           Q        R

3.        •────────────→
           S          T

4.        •────────────•
           U          V

Step 1: Look at the markings.

  • Figure 1 has only one dot, so it is a point: PP.
  • Figure 2 has arrowheads on both ends, so it extends forever in both directions. It is a line: QR\overleftrightarrow{QR}.
  • Figure 3 has one endpoint at SS and an arrowhead pointing right, so it is a ray: ST\overrightarrow{ST}. The endpoint is named first.
  • Figure 4 has two endpoints and no arrowheads, so it is a segment: UV\overline{UV}.

Remember: The drawing of a line or ray shows only part of it. The arrowhead means that the figure continues forever in that direction.

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Identify Lines, Segments, and Rays


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