If four points are collinear, they are also coplanar. A. True B. False
The Correct Answer and Explanation is:
Correct Answer: A. True
When four points are collinear, they lie along the same straight line. A line, by definition, exists entirely within a single plane. Therefore, if all four points are located on the same line, they must also reside within the same plane. This means they are not only collinear but also coplanar.
To understand this better, consider the definitions:
- Collinear points are points that lie on the same straight line.
- Coplanar points are points that lie on the same geometric plane.
A plane is a flat, two-dimensional surface that extends infinitely in all directions. Every line lies in at least one plane. Since a line is a part of a plane, any set of points along that line also lies within that plane. Therefore, four collinear points automatically satisfy the requirement of being in the same plane, making them coplanar.
This relationship holds regardless of how far apart the points are, or their order. As long as they are all on the same straight line, they are part of the same geometric plane. No additional condition or construction is needed to establish coplanarity in this case.
In contrast, four non-collinear points may or may not be coplanar. Three points always determine a plane, but the fourth point must lie in the same plane as the first three to be considered coplanar. That condition does not apply when all points are collinear because a line inherently lies in a single plane.
Thus, whenever four points are collinear, it can be concluded with certainty that they are also coplanar. This makes the statement true.
