Question

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.

Explanation:

Step1: Recall centroid property

The centroid of a triangle divides each median in a ratio of 2:1, where the distance from the vertex to the centroid is twice the distance from the centroid to the mid - point of the opposite side.

Step2: Analyze given lengths

Given $JG = 5$ cm and $GE=10$ cm. The ratio of $GE$ to $JG$ is $\frac{GE}{JG}=\frac{10}{5} = 2:1$.

Answer:

Point G can be a centroid because GE and JG are in the ratio 2:1.