Final answer:
The centroid of a triangle divides the median into a 2:1 ratio. UZ is two thirds of the median, so to find the full length UY, we multiply UZ (8) by 3/2 to get 12.
Step-by-step explanation:
The question involves finding the length of segment UY when given that Z is the centroid of triangle UVW and UZ has a length of 8. In a triangle, the centroid divides each median into two segments, the shorter segment, from the centroid to the vertex, being one third the length of the median, and the longer segment, from the centroid to the midpoint of the opposite side, being two thirds the length.
Since UZ is part of the median and Z is the centroid, UZ is two thirds of the length of the median from U to Y. Therefore, to find the full length of the median (UY), we can use the formula:
Median = 3/2 x (length of segment from centroid to vertex)
In this case:
UY = 3/2 x UZ
UY = 3/2 x 8
UY = 12
Hence, the length of UY is 12, which corresponds to option D.