In the diagram, JG is equal to 5 cm and GE is equal to 10 cm. Based on this information, can cap g be a centroid of triangle HJK ?
Answer
A
Point cap g can be a centroid because GE and JG are in the ratio ratio of 2 to 1 .
B
Point cap g can be a centroid because JG plus GE is equal to JE .
C
Point cap g cannot be a centroid because JG and GE are in the ratio ratio of 1 to 2 .
D
Point cap g cannot be a centroid because JG does not equal GE .
Explanation
A centroid divides each median so the distance from the vertex to the centroid is twice the distance from the centroid to the midpoint of the opposite side. Here JG:GE = 5:10 = 1:2, not 2:1, so G cannot be the centroid. The correct choice is D: JG and GE are in the ratio 1 to 2.
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