What determines if three randomly selected points from a rectangular coordinate system can form a triangle?

To determine if three randomly selected points in a rectangular coordinate system can form a triangle, the key condition is that the points must not be collinear, meaning they cannot all lie on the same straight line. When points are collinear, they do not form a triangle; instead, they lie along a single line without any area.

Understanding this concept, option B is correct because if all three points are on the same line, they fail to create a triangle. The area that a triangle occupies is defined by points that extend outward from a base formed between two of the points, while the third must not fall along that same straight line to maintain the triangular shape.

In contrast, the other choices describe conditions that either do not relate directly to the formation of a triangle or imply configurations that would not prevent collinearity. For instance, having different x-coordinates does not guarantee that the points are not collinear, as they could be arranged vertically. Similarly, being adjacent points does not ensure they will be non-collinear, and being equally spaced matters less than the actual geometrical positioning in relation to one another. Hence, the critical understanding lies in ensuring points are non-collinear, which confirms option B as the valid answer.