Question

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.

Explanation:

Step1: Propiedad del centroid

El centroid de un triángulo divide a cada mediana en una razón de \(2:1\). Esto significa que si \(FG = 6\) cm y \(FC=18\) cm, entonces \(GC=FC - FG=18 - 6 = 12\) cm.

Step2: Verificar la razón

La razón \(GC:FG=\frac{12}{6}=2:1\)

Answer:

Point G can be the centroid because \(12:6\) equals \(2:1\)