Which statement is true about the relationship between points and planes in three-dimensional space?

• A. A single $\mathrm{point}$ is sufficient to define a unique $\mathrm{plane}$.
• B. Four $\mathrm{points}$ always determine a unique $\mathrm{plane}$.
• C. Two distinct $\mathrm{points}$ always determine a unique $\mathrm{plane}$.
• D. Three non-collinear $\mathrm{points}$ determine exactly one $\mathrm{plane}$.

Answer: (D)

Verified step by step guidance

1. Recall the fundamental concept in three-dimensional geometry: a plane is uniquely determined by three points that are not collinear (i.e., they do not all lie on the same straight line).
2. Understand why a single point is not enough: one point can be part of infinitely many planes passing through it, so it cannot define a unique plane.
3. Consider two distinct points: while they define a unique line, infinitely many planes can contain that line, so two points do not determine a unique plane.
4. Examine four points: if the points are coplanar (all lie on the same plane), they determine that plane; if not, no single plane contains all four points, so four points do not always determine a unique plane.
5. Conclude that the correct statement is that three non-collinear points determine exactly one unique plane, because these points fix the plane's position and orientation in space.