Final answer:
Colinear points cannot define a plane because they do not provide the necessary shape or area, such as a triangle does, to establish a plane's dimensions and orientation in three-dimensional space.
Step-by-step explanation:
Three colinear points do not define a plane because they lie on a single line and therefore cannot establish a unique plane. A plane in a three-dimensional space requires at least three non-colinear points to define its dimensions and orientation. This is because only non-colinear points provide the needed information to create a shape that has area, such as a triangle, which can be extended into a plane. With colinear points, there is no angle or area to expand upon, making it impossible to define the boundaries of a plane. Instead, we can use non-colinear points to create a triangle, as a triangle is a figure with three sides lying on a plane with each of its three angles adding up to 180 degrees, demonstrating the concept of defining a plane with non-colinear points.