Final answer:
Leon was correct in saying that hk is the perpendicular bisector of gj if h is equidistant from the endpoints of gj and hk is perpendicular to gj.
Step-by-step explanation:
If point h is equidistant from the endpoints of line segment gj, then point h is the midpoint of gj. For hk to be the perpendicular bisector of gj, hk must satisfy two conditions: first, hk must be perpendicular to gj, which means it forms a 90º angle with gj; second, hk must bisect gj, which means it cuts gj into two equal parts at h. If these conditions are met, which is implied by the description, then hk is indeed the perpendicular bisector of gj as Leon said. The fact that h is equidistant from g and j indicates that it bisects the segment, and if hk is known to be perpendicular as well, then it qualifies as a perpendicular bisector.