https://file.aiquickdraw.com/mathbot/file/172615127945616if0th2.jpg

The image presents a number line with three points: \( A \), \( B \), and \( C \), located at coordinates \( -3 \), \( 1 \), and \( 6 \), respectively. There are four statements, and we need to identify which ones are true based on this number line.

Let’s evaluate each statement:

**A. The length of \( \overline{AB} \) is \( -3 \).**
- The length of \( \overline{AB} \) is calculated as the distance between \( A \) and \( B \). This is \( |1 - (-3)| = |1 + 3| = 4 \). Length cannot be negative, so this statement is **false**.

**B. \( d(B, C) = BC = |6 - 1| \)**
- The distance between \( B \) and \( C \) is \( |6 - 1| = 5 \). This statement is **true**.

**C. \( AB + AC = BC \)**
- We know that \( AB = 4 \) and \( AC = |6 - (-3)| = |6 + 3| = 9 \), but \( BC = 5 \).
- So, \( AB + AC = 4 + 9 = 13 \), which is not equal to \( BC \). This statement is **false**.

**D. \( AB + BC = AC \)**
- Here, \( AB = 4 \), \( BC = 5 \), and \( AC = 9 \). Since \( AB + BC = 4 + 5 = 9 \), and \( AC = 9 \), this statement is **true**.

### Conclusion:
- The correct answers are **B** and **D**.

Would you like further clarification or additional details?

Here are 5 related questions for further practice:
1. How do you calculate the distance between two points on a number line?
2. Why can’t the length of a line segment be negative?
3. What is the formula for the distance between two points in a plane?
4. How can we check if three points are collinear?
5. What is the significance of the absolute value in distance calculations?

**Tip:** Always use absolute value when calculating distances, as distance is always non-negative.

Which of the following statements are true? Select all that apply.

Learn how to calculate the distance between points A, B, and C on a number line and determine which statements about segment lengths are true. This problem introduces concepts such as absolute value and the segment addition postulate. Ideal for Grades 6-8.

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