In the xy–coordinate plane, a line segment is drawn to join the points

Dear robu,
I'm happy to respond. I'm curious about the source. This feels not so much like a real GMAT question, but more like a review question from a review book about introductory coordinate geometry problems. This is about seven notches easier than an actual GMAT question.

Once a line is specified, then obviously specifying either the x- or y-coordinate of the point will specify the exact point on the line, which will full establish whether the point is the midpoint.

Also, here's a diagram. The fact that this line has a slope of one and involves three consecutive lattice points is further evidence of how simplistic this question is:


Everything is significant. Answer = (D).

For coordinate geometry questions that are significantly more test-like, see:
Challenging Coordinate Geometry Practice Questions

Mike