Final answer:
Three points define a flat surface and thus always form a plane, while the introduction of a fourth point could deviate from that plane, introducing a three-dimensional aspect. Only two lines are required to define a point in a plane, but three coordinates are needed in a three-dimensional space.
Step-by-step explanation:
Three points always form a plane because they can define a flat surface. When you conceptualize a triangle, you're essentially visualizing a three-sided figure with three angles that add up to 180 degrees, which lies on a single plane. However, when introducing a fourth point, there's no guarantee that this point will lie on the same plane as the first three points. This fourth point can either lie on that plane or deviate from it, leading to a three-dimensional shape.
In geometry, only two lines are necessary to define a point in a plane. Extending this to three dimensions, a single point can be completely determined with three coordinates (x, y, z) while having the liberty to move gratuitously in the third dimension. This explains how three points can easily form a plane by providing fixed coordinates on a two-dimensional level, but with four points, the additional point brings in the third dimension which creates more complexity.