1)Z lies on the perpendicular bisector of line segment XY. 2) Z also lies on the cicumferences of the circles formed by taking line segment $\overline{XY}$ and line segment $\overline{YX }$ as radii. Edit :- 5 vertices are to be excluded from the vertices I mentioned above. Those vertices are :- 1) Mid point of line segment XY. 2) The extreme end points of line segments $\overline{XY}$ and $\overline{YX}$ produced its own lengths. 3) Last but not the least vertices X and Y of course.