In triangle ABC , the segments drawn from the vertices intersect at point cap g Segment FG measures 6 cm, and segment FC measures 18 cm. Which best explains whether point cap g can be the centroid?
Answer
A
Point cap g can be the centroid because FC is longer than FG .
B
Point cap g cannot be the centroid because FG should be longer than CG .
C
Point cap g cannot be the centroid because ratio of 18 to 6 does not equal ratio of 2 to 1 .
D
Point cap g can be the centroid because ratio of 12 to 6 equals ratio of 2 to 1 .
Explanation
A centroid divides each median so the segment from a vertex to the centroid is twice the segment from the centroid to the midpoint of the opposite side. Since FC is 18 cm and FG is 6 cm, CG = 18 − 6 = 12 cm. The ratio CG:GF is 12:6, or 2:1, so point G can be the centroid; this matches choice D.
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