Question

Which expressions show the distance between points A and B on the number line?

Select all that apply.

4 5 6

3

2

1

0

21

22

23

24

25

26

A

B

햠 |25| 1 4

a -5 + 4

b |4+ (-5)|

c 4- |-5|

d 4-(-5)

Answer 1

To find the distance between points A and B on the number line, you can use the formula for distance between two points \( A \) and \( B \):

\[ \text{Distance} = |A - B| \]

To assess the given expressions, let's decode each option:

1. **a |25| - 14**: This expression calculates the absolute value of 25, then subtracts 14. It does not evaluate the distance between two points A and B; thus, it does not apply.

2. **b |4 + (-5)|**: This expression simplifies to |4 - 5| = | -1 | = 1. This gives the absolute distance between the two values, which aligns with the distance concept. This applies.

3. **c 4 - |-5|**: This expression simplifies to 4 - 5 = -1. Since distance cannot be negative, and this does not reflect the distance formula, this does not apply.

4. **d 4 - (-5)**: This expression simplifies to 4 + 5 = 9. This is the sum of two numbers and does not represent the distance formed by absolute value or subtraction required for distance on a number line, so it does not apply.

### Therefore, the correct option showing the distance between points A and B is:
- **b |4 + (-5)|**