Final answer:
Three points determine a plane when they are non-collinear, meaning they do not all lie on the same line. Collinear points define a line, not a plane, so the correct answer is 'They are non-collinear'.
Step-by-step explanation:
To describe three points so that they determine a plane, you need to ensure that they satisfy certain conditions. Specifically, for three points to determine a plane, they must not lie on the same line; in other words, the three points must be non-collinear. If the points were collinear, they would lie on a single line and not be able to define a plane.
Looking at options A and B — stating that the points either 'lie on a line' or 'are collinear' — we can see that neither of these cases would define a plane, as a line is a one-dimensional construct, while a plane is two-dimensional. Option D, which suggests the points are on 'different planes', would also not allow the points to determine a single plane together. Thus, the correct answer is option C, stating that the points are 'non-collinear', ensuring that they do not all lie on the same line and therefore can indeed define a plane in three-dimensional space.