To solve the problem of finding the length of segment $j$, which is the midline of trapezoid $ABCD$:

Step-by-Step Explanation:

1. Midline of a Trapezoid Formula: The length of the midline $j$ in a trapezoid is the average of the lengths of the two parallel bases. The formula is: $j = \frac{\text{Base}_1 + \text{Base}_2}{2}$

2. Identify the Bases: From the diagram:

   • $\text{Base}_1 = AB = 10.3$
   • $\text{Base}_2 = CD = 23.1$

3. Calculate the Length of $j$: Substitute the values into the formula: $j = \frac{10.3 + 23.1}{2} = \frac{33.4}{2} = 16.7$

4. Final Answer: The length of segment $j$, rounded to 1 decimal place, is: $\boxed{16.7}$

Let me know if you want further clarification or have any other questions!

Here are five related questions to expand your understanding:

1. What happens if the bases are not given, and you only know the height and the area?
2. How does the formula change for different types of trapezoids, like isosceles trapezoids?
3. Can you find the length of $j$ if the bases are given in a different unit (e.g., meters instead of centimeters)?
4. What other properties of trapezoids rely on the midline?
5. How can this formula help when solving for unknown side lengths of a trapezoid?

Tip: Always verify that you correctly identify the parallel bases when using this formula, as incorrect identification can lead to errors.