Question

Triangle A B C is shown. Lines are drawn from each point to to the opposite side and intersect at point G. Line segments A D, B E, and C F are created.
In triangle ABC, the segments drawn from the vertices intersect at point G. Segment FG measures 6 cm, and segment FC measures 18 cm.

Which best explains whether point G can be the centroid?

Point G cannot be the centroid because 18:6 does not equal 2:1.
Point G cannot be the centroid because FG should be longer than CG.
Point G can be the centroid because 12:6 equals 2:1.
Point G can be the centroid because FC is longer than FG.

Answer 1

Correct answer: "Point G can be the centroid because 12:6 equals 2:1."

Explanation: If CF = 18 and FG = 6, then CG = CF − FG = 12. The centroid divides a median so CG:GF = 2:1; here 12:6 = 2:1, so G can be the centroid.