Key takeaway: A ray is a straight figure with one fixed endpoint that stretches without end in a single direction, always named by listing the endpoint first and then one more point on it.
Grade 10 – GeometryG-CO.A.1Geometry and Measurement
Definition of Ray
A ray works like a laser pointer shining into space. The pointer is the fixed start, and the beam never stops: one endpoint, then an unending path in one direction.
Two such figures leaving the same point in exactly opposite directions are called opposite rays, and together they trace a full line. Two that leave a shared point in different directions are the sides of an angle.
Formula and notation
The symbol \(\vec{AB}\) names the figure that starts at \(A\) and passes through \(B\). Order matters:
\[ \vec{AB} \neq \vec{BA} \]
The arrow points away from the starting point, and the starting point is always the first letter written.
Key facts
- The first letter in the name is always the point where the figure begins.
- It has no length, because it never ends in its direction of travel.
- Opposite rays share their starting point and together form a straight line.
- Any point on it, other than the start, can serve as the second letter.
Ray example
On a trail map, mile markers \(K\), \(L\) and \(N\) sit on one straight path in that order, west to east. Name the ray that begins at \(L\) and heads east, then name the one that begins at \(L\) and heads west. Does \(\vec{KL}\) include marker \(N\)?
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Beginning at \(L\) and heading east passes through \(N\), so the name is \(\vec{LN}\).
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Beginning at \(L\) and heading west passes through \(K\), so the name is \(\vec{LK}\).
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\(\vec{KL}\) begins at \(K\), crosses \(L\) and never stops heading east, so it contains \(N\).
The two names are \(\vec{LN}\) and \(\vec{LK}\), and yes, \(\vec{KL}\) includes \(N\).
Common mistake
Watch out
Tia writes \(\vec{NL}\) for the figure that begins at \(L\) and goes through \(N\).
Why it is wrong
The name lists the starting point first. \(\vec{NL}\) begins at \(N\) and heads west through \(L\) and \(K\), a different ray. The correct name is \(\vec{LN}\).
Related terms and lessons
Browse the glossary: A–Z list · Geometry vocabulary · Geometry and Measurement