Given that A is between Y and Z, and that YA = 5.5, AZ = 2x, and YZ = 41.5, find AZ.


We are given the following information:

- Point \( A \) is between points \( Y \) and \( Z \).
- \( YA = 5.5 \)
- \( AZ = 2x \)
- \( YZ = 41.5 \)

Since \( A \) is between \( Y \) and \( Z \), we can apply the segment addition postulate, which states:

\[
YA + AZ = YZ
\]

Substituting the given values into this equation:

\[
5.5 + 2x = 41.5
\]

### Step 1: Solve for \( x \)

\[
2x = 41.5 - 5.5
\]
\[
2x = 36
\]
\[
x = \frac{36}{2} = 18
\]

### Step 2: Find \( AZ \)

Now, substitute \( x = 18 \) back into the expression for \( AZ \):

\[
AZ = 2x = 2(18) = 36
\]

Thus, \( AZ = 36 \).

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Would you like more details or have any questions?

Here are 5 related questions to consider:
1. If \( A \) were exactly in the middle of \( Y \) and \( Z \), what would the values of \( YA \) and \( AZ \) be?
2. Can you solve for \( YA \) if \( AZ = 41.5 - 5.5x \)?
3. How would the equation change if \( A \) was outside the segment \( YZ \)?
4. What if the total distance \( YZ \) was unknown, but you knew \( AZ \) and \( YA \)?
5. Could you write a general formula for any three points on a line with known distances?

**Tip:** Always double-check units or dimensions when solving problems with distances.

Given that A is between Y and Z, and that YA = 5.5, AZ = 2x, and YZ = 41.5, find AZ.

Solve the problem involving points Y, A, and Z on a line where YA = 5.5, AZ = 2x, and YZ = 41.5. Using algebra and the segment addition postulate, this step-by-step guide shows how to find AZ. Suitable for Grades 6-8 students.

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