Question

Triangle J K L is shown. Lines are drawn from each point to the opposite side and intersect at point P. Line segments J O, K M, and L N are created.
In the diagram, which must be true for point P to be the centroid of the triangle?

LN ⊥ JK, JO ⊥ LK, and JL ⊥ MK.
JL = LK = KJ
JM = ML, LO = OK, and KN = NJ.
LN is a perpendicular bisector of JK, JO is a perpendicular bisector of LK, and MK is a perpendicular bisector of JL.

Answer 1

Correct answer: JM = ML, LO = OK, and KN = NJ.

Reason: The centroid is the point where the three medians meet. A median connects a vertex to the midpoint of the opposite side, so each of M, O, N must be the midpoint of the opposite side (JM = ML, LO = OK, KN = NJ). The other choices describe the orthocenter (perpendiculars), a special equilateral case (not required), or the circumcenter (perpendicular bisectors).