Question

Triangle H J K is shown. Lines are drawn from each point to the opposite side and intersect at point G to form line segments H C, J E, and K D.
In the diagram, JG = 5 cm and GE = 10 cm. Based on this information, can G be a centroid of triangle HJK?

Point G cannot be a centroid because JG does not equal GE.
Point G cannot be a centroid because JG and GE are in the ratio 1:2.
Point G can be a centroid because GE and JG are in the ratio 2:1.
Point G can be a centroid because JG + GE = JE.

Answer 1

Answer: Point G cannot be a centroid because JG and GE are in the ratio 1:2.

Reason: The centroid divides a median in a 2:1 ratio measured from the vertex (vertex→centroid : centroid→midpoint = 2:1). Here JG:GE = 5:10 = 1:2, the opposite ratio, so G cannot be the centroid.