https://file.aiquickdraw.com/mathbot/file/17259522682176as8it23.jpg

The problem in the image can be broken down as follows:

We are given two points \( A \) and \( B \) on a number line. The distance between \( A \) and \( B \) is 11, i.e., \( AB = 11 \), and we know that point \( B \) is located at 8.

### Step-by-step solution:

The distance between two points on a number line is the absolute difference between them:
\[
|A - B| = 11
\]
We know that \( B = 8 \), so:
\[
|A - 8| = 11
\]

To solve this, we need to consider two cases, since the absolute value gives two possible solutions:
1. \( A - 8 = 11 \)
2. \( A - 8 = -11 \)

#### Case 1:
\[
A - 8 = 11 \implies A = 11 + 8 = 19
\]

#### Case 2:
\[
A - 8 = -11 \implies A = -11 + 8 = -3
\]

Thus, the possible locations for \( A \) are **19** and **-3**.

### Final Answer:
\( A \) could be located at 19 or -3.

Would you like further details or have any questions?

Here are 5 related questions to expand on this:
1. How do you calculate the distance between two points on a number line?
2. What happens if the distance is given as a negative number? Is that possible?
3. How can you apply this concept to points in 2D or 3D space?
4. How does the absolute value function affect equations like this?
5. If \( B \) were located at a different point, how would the possible values of \( A \) change?

**Tip**: Always check both the positive and negative cases when solving absolute value equations.

Suppose that A and B are points on the number line. If AB = 11 and B lies at 8, where could A be located?

Learn how to locate point A on a number line given that the distance between points A and B is 11, with B located at 8. This problem covers concepts of absolute value equations and number line positioning, suitable for students in Grades 6-8.

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