What is a Ray in Geometry? — Definition & Examples
Ray definition in geometry
A ray is part of a line. Rays have a fixed starting point and no end point. A ray extends in only one direction infinitely. The ray's starting point and another point along the ray are used to name the ray in geometry.
| Property | Description |
|---|---|
| Starting Point | Fixed endpoint where the ray begins |
| End Point | None; extends infinitely in one direction |
| Direction | One way only |
| Naming Convention | Endpoint listed first, then another point on the ray |
| Symbol | A one-way arrow drawn above two capital letters |
Find an LED flashlight. Go into a dark room and turn the flashlight on. You have just modeled a ray, a plane figure in geometry that has one endpoint but continues in the other direction forever. Rays and real-life examples of rays are all around us.
How to draw a ray
To draw a ray, place two points on a piece of paper. Label both points with capital letters. Choose one point to be the endpoint. Use a straightedge to draw a line starting at your endpoint and continuing through your second point. Draw one arrowhead on the open end of your line (the one opposite the endpoint).
Ray symbol and label
To symbolize and label a ray, we need that endpoint identified. We also need some other point along the one-way line. Then, we write the endpoint and other point together as capital letters, capped by a tiny, one-way arrow (pointing to the right):
| Element | Description |
|---|---|
| Endpoint | Written as the first capital letter in the ray's name |
| Second Point | Any other point on the ray, written as the second capital letter |
| Arrow Symbol | A small one-way arrow above the two letters, pointing right |
This symbol for a ray can be compared to an NFL quarterback's throw. A strong, short pass travels so fast that gravity barely tugs the football down, making it look like a straight-line ray. The quarterback is the endpoint; the traveling football traces the one-way line.
Ray in geometry examples
A ray of sunshine is a ray. It originates at our star, the Sun, and travels one way, striking Earth some eight minutes after it left its "endpoint," the Sun.
| Real-Life Example | Endpoint | Direction of Travel |
|---|---|---|
| Sunlight | The Sun | Outward through space, reaching Earth |
| Tennis serve (e.g., Carlos Alcaraz at ~230 kph / 143 mph) | Racket at point of contact | Across the court in a near-straight line |
| Classroom projector beam | Projector lens | Toward the screen |
| Arrow from a bow | Bow upon release | Toward the target |
| Laser beam | Laser source | Steady, straight one-way line |
Tennis pro Carlos Alcaraz famously serves tennis balls at speeds reaching roughly 230 kph (143 mph), which defies gravity's tug so well the ball seems to travel in a straight line, just like a ray.
The light beam from a classroom LCD projector is a ray; so is light from a movie projector at your local cinema.
The path an arrow travels from a bow is a ray and has the added benefit of being, well, arrow-shaped.
Lasers are excellent examples of rays because, unlike sports balls, they are not significantly affected by Earth's gravity. They shine in steady, straight one-way lines from their source.
A word of caution
Because English-language speakers, readers, and writers move their eyes from left to right, almost all rays you see symbolized in mathematics will have left endpoints and right arrows. Keep in mind, though, geometry is a pure science. Rays can go in any direction: up, down, left, right, or diagonally.