Ray
In short: A ray begins at a single endpoint and then extends without end in one direction along a straight path, so it has a starting point but no measurable length.
GeometryGeometryG-CO.A.1
What is Ray?
Picture a flashlight beam that begins at the bulb and never stops: that is a ray. It has exactly one endpoint, its starting point, and runs without end in one direction.
The name lists the endpoint first, then any other point on the path. The symbol \(\overrightarrow{AB}\) starts at \(A\) and passes through \(B\), while \(\overrightarrow{BA}\) starts at \(B\) and passes through \(A\), a different figure. Two of them with a shared endpoint that point in opposite directions along one line are called opposite rays.
How to spot it
- A diagram shows an arrowhead on one end of a straight path and a solid dot on the other end.
- The notation has a half-arrow over two letters, such as \(\overrightarrow{MN}\), with the arrowhead pointing right.
- A problem describes a laser, a sightline or a headlight beam that starts at a source and keeps going.
- The two sides of a corner are drawn from one common vertex, each continuing without end.
The method
- Locate the endpoint and write its letter first in the name.
- Choose any second point that the path passes through and write that letter next: \(\overrightarrow{AB}\).
- On a number line, decide the direction from the second point, then check which side of the endpoint a coordinate falls on.
- For opposite rays, confirm they share the endpoint and that the pair lies along one straight path.
Ray: solved example
Problem
On a number line, a path starts at \(-4\) and passes through \(3\). Which of the coordinates \(-9\), \(-4\), \(0\) and \(12\) lie on it?
Solution
Since \(3 > -4\), the path heads toward larger numbers. It contains every coordinate greater than or equal to \(-4\).
Test each one: \(-9 < -4\), so it is off; \(-4\) is the endpoint, so it is on; \(0\) and \(12\) are larger, so they are on. The coordinates on it are \(-4\), \(0\) and \(12\).
Try it
Question 1
Are \(\overrightarrow{PQ}\) and \(\overrightarrow{QP}\) the same figure?
Show the answer
No. The first starts at \(P\) and goes through \(Q\); the second starts at \(Q\) and goes through \(P\), heading the other way.
Question 2
A path starts at \(7\) on a number line and passes through \(1\). Is the coordinate \(15\) on it?
Show the answer
It heads toward smaller numbers, so only coordinates at most \(7\) belong. Since \(15 > 7\), it is not on the path.
Ray vs. Line Segment
A segment owns two endpoints and a size you can state, such as 36 inches. A ray owns one endpoint and never stops, so no length can be assigned to it. Both are slices of a line: \(\overline{AB}\) halts at B, whereas \(\overrightarrow{AB}\) sails on beyond B.
Keep going
Lessons
Worksheets and quizzes
Related words
Whole dictionary: A–Z · Geometry · Geometry