Answer
$ZU = \frac{27}{2}$
$ZY = \frac{9}{2}$
Work Step by Step
According to the concurrency of medians theorem, the medians of a triangle are concurrent at a point that is two-thirds of the way between each vertex and the midpoint of the side opposite to the vertex.
$\overline{ZY}$ is one-third of the way from $U$ to $Z$. Let's set up an equation incorporating what we know:
$YU = \frac{2}{3}(ZU)$
Let's plug in what we know:
$9 = \frac{2}{3}(ZU)$
Divide each side by $\frac{2}{3}$ to solve for $TW$. To divide by $\frac{2}{3}$ means to multiply by its reciprocal, which is $\frac{3}{2}$:
$ZU = 9(\frac{3}{2})$
Multiply to solve:
$ZU = \frac{27}{2}$
If $ZU$ is the sum of $YU$ and $ZY$, we can subtract $YU$ from $ZU$ to get $ZY$:
$ZY = ZU - YU$
Let's plug in what we know:
$ZY = \frac{27}{2} - 9$
Rewrite $9$ as an equivalent fraction with $2$ as its denominator:
$ZY = \frac{27}{2} - \frac{18}{2}$
Subtract to solve:
$ZY = \frac{9}{2}$
