Answer
$VY = 6$
$YX = 3$
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.
$\overline{YX}$ is one-third of the way from $V$ to $X$. Let's set up an equation incorporating what we know:
$VY = \frac{2}{3}(VX)$
Let's plug in what we know:
$VY = \frac{2}{3}(9)$
Multiply to solve for $VY$:
$VY = \frac{18}{3}$
Divide both the numerator and denominator by their greatest common factor, which is $3$:
$VY = 6$
If $VX$ is the sum of $VY$ and $YX$, we can subtract $VY$ from $VX$ to get $YX$:
$YX = VX - VY$
Let's plug in what we know:
$YX = 9 - 6$
Subtract to solve:
$YX = 3$
