You are correct. The answer is choice A.
The ray extends infinitely in one direction.
That direction being toward point C. If you wanted the ray to extend in both directions, then it would be a line and not a ray. This would rule out choice C.
Since the ray is infinitely long, we cannot measure its length. The length goes on forever. This rules out choice D.
Choice B can be ruled out because there are infinitely many points on any line, line segment, or ray. Simply apply the midpoint rule to find a new point in between any two points. This process can go on forever.