A line and two points are guaranteed to be coplanar if: A. they lie in the same plane. B. they are near each other. C. one point and the line are coplanar. D. they don't lie in the same plane.

If you have a line and two points that lie within the same plane, you're all set for them to be coplanar. So, A is the correct choice! It's like having a table (the plane) and placing a pencil (the line) along with some fun toys (the points) right on top. They all share the same space! Now, understanding the importance of this concept is vital when dealing with geometry problems in real life, like designing a park with pathways or ensuring your home's layout fits together smoothly. If the line and points you're working with aren't coplanar, it can lead to some serious misalignment issues!