Final answer:
Any three coplanar points are not necessarily collinear. A counterexample is the vertices of a triangle, which are coplanar but not collinear.
Step-by-step explanation:
The statement that any three coplanar points are also collinear is not always true, as a counterexample can be found by considering any three points that form the vertices of a triangle. A triangle is a three-sided figure lying on a plane with three angles adding up to 180 degrees, and its vertices are not collinear by definition since they form the corners of the shape.
As an example, in the Cartesian plane, take three points A(0,0), B(0,1), and C(1,0). These points form a right triangle and are clearly coplanar, as they all lie on the x-y plane. However, they are not collinear since they do not lie on the same line.
It is essential to differentiate between coplanar points, which are points all lying on the same plane, and collinear points, which are points all lying on the same straight line. While all collinear points are also coplanar (assuming they are in the same plane), not all coplanar points are collinear.