Answer:
JQ = 48
QA = 24
Step-by-step explanation:
The centroid is the intersection of three segments that goes from the vertex to the midpoint of the opposite side called medians. In this case, the centroid is point Q.
By the centroid theorem, the distance from the vertex to the centroid is 2/3 the distance of the complete segment.
So, in this case, JQ = (2/3)JA
Because JQ goes from the vertex to the centroid and JA is the complete segment.
Replacing JA by 72, we get:
JQ = (2/3)(72)
JQ = 48
It is also equivalent to say that QA = (1/3)JA
Because QA is the distance from the centroid to the midpoint.
QA = (1/3)(72)
QA = 24