To determine which statement is true, let's analyze each option step by step using our knowledge of geometry:
Option A: "At least three points are needed to determine a line."
This statement is not true. In geometry, only two distinct points are required to determine a unique line—the line that passes through both points. No additional points are necessary.
Option B: "A ray consists of two endpoints and all the points between them."
This statement is also not true. By definition, a ray has only one endpoint (the point where the ray starts) and it extends infinitely in one direction from that endpoint. Unlike a line segment, which has two endpoints, a ray does not have a second endpoint.
Option C: "A ray is a set of points that extends infinitely in both directions."
This statement is incorrect. The definition given in Option C is actually the definition of a line. A ray, as mentioned earlier, starts at a single point (the endpoint) and extends infinitely in one direction.
Option D: "A line is a set of points that extends infinitely in both directions."
This statement is true. According to the definitions in geometry, a line is exactly that—a straight one-dimensional figure that extends without end in both directions. It has no thickness and is defined by an infinite set of points that lie along its length.
Therefore, the correct statement is Option D: "A line is a set of points that extends infinitely in both directions."
