Question

which pair of undefined terms is used to define a ray?
line and plane
plane and line segment
point and line segment
point and line

Explanation:

To determine the pair of undefined terms used to define a ray, we first recall the definitions of undefined terms in geometry (point, line, plane) and the definition of a ray. A ray is defined as a part of a line that starts at a point (the endpoint) and extends infinitely in one direction.

• A line is an undefined term that extends infinitely in both directions.
• A point is an undefined term that represents a location.

To define a ray, we need a point (to serve as the endpoint) and a line (to provide the infinite direction, with the ray being a portion of the line starting at the point and going infinitely in one direction).
Now let's analyze the options:

• "line and plane": A plane is not involved in defining a ray, so this is incorrect.
• "plane and line segment": A plane and a line segment (which is a defined term with two endpoints) are not used to define a ray, so this is incorrect.
• "point and line segment": A line segment has two endpoints and is a defined term, and it doesn't help in defining a ray (which is infinite in one direction), so this is incorrect.
• "point and line": A point (endpoint) and a line (to get the infinite direction, with the ray being part of the line starting at the point) are used to define a ray, so this is correct.

Answer:

D. point and line