To solve this problem, we utilize the fact that B is the centroid of triangle △CDE. A centroid divides each median of the triangle into a 2:1 ratio, with the longer segment being closer to the vertex of the triangle.

Step-by-Step Solution:

1. Identify the relevant median:

The median $JD$ in the diagram connects vertex $D$ to the midpoint of side $CE$. Since $B$ is the centroid, the segment $JD$ is divided such that: $JB : BD = 1 : 2$ This means that $JB$ is one-third of $JD$, and $BD$ is two-thirds of $JD$.

2. Use the given length $BD = 4.6$:

From the 2:1 ratio, we know: $BD = \frac{2}{3} JD$ Substitute $BD = 4.6$: $4.6 = \frac{2}{3} JD$

3. Solve for $JD$:

Multiply both sides by $\frac{3}{2}$ to isolate $JD$: $JD = 4.6 \cdot \frac{3}{2}$ $JD = 6.9$

Final Answer:

The length of $JD$ is 6.9 units.

Do you want me to verify or explain any specific step further?

Here are 5 questions to deepen your understanding:

1. What is the definition and role of the centroid in a triangle?
2. How can the 2:1 centroid property be applied to other medians?
3. How would the solution change if a different median was involved?
4. What is the significance of dividing a triangle's median into specific ratios?
5. How can we calculate the midpoint of $CE$ geometrically if coordinates were given?

Tip: The centroid always divides a triangle into six smaller triangles of equal area!