Four points are always coplanar if:
Check all that apply.
A. they lie in the same plane.
B. they are collinear.
C. they lie on different planes.
D. they lie on different lines.
The correct answer and explanation is :
Correct Answers:
✅ A. they lie in the same plane
✅ B. they are collinear
Explanation:
In geometry, coplanar points are points that lie on the same plane. A plane is a flat, two-dimensional surface that extends infinitely in all directions. For any set of points to be considered coplanar, they must all exist within one such flat surface.
Let’s examine each option:
✅ A. They lie in the same plane
This is always true by definition. If four points lie in the same plane, then they are coplanar. This is the most straightforward and literal interpretation of what it means to be coplanar.
✅ B. They are collinear
This is also true. Collinear points lie on the same straight line. A line itself lies entirely on a single plane. Therefore, any set of collinear points is also coplanar, because they share the same plane through the line.
Even more specifically, a single line always exists within a plane, so if four points are on the same line, then that line — and thus those points — must lie in one plane.
❌ C. They lie on different planes
This is false. If the four points lie on different planes, then they cannot all exist in one common plane, which violates the definition of coplanar. Only if all four points share at least one plane are they considered coplanar.
❌ D. They lie on different lines
This can be true or false, depending on the relative position of the lines. If the lines are non-coplanar (like skew lines in 3D space), then the points on them might not be coplanar. Thus, this statement is not always true, so it does not qualify.
Summary:
The only statements that are always true for four points to be coplanar are:
- A. They lie in the same plane.
- B. They are collinear.