Question

On a number line, what is the distance between −9 and -5? Choose all the correct answers.

A) -14
B) -4
C) 4
D) | -5 - (-9) |
E) | -9 - (-5) |
F) 14

Answer 1

The distance between −9 and −5 on a number line is 4, represented by the absolute values | −5 − (−9) | and | −9 − (−5) |. Options C, D, and E are correct.

Step-by-step explanation:

To find the distance between −9 and −5 on a number line, you essentially count the number of units between the two points. The distance between two points on a number line is always a positive number because distance is a measure of the length between two points and cannot be negative.

Calculate the distance using subtraction, always considering the absolute value since distance is non-negative. When we subtract −5 from −9 (−5 − (−9)), we get 4. We can also calculate the distance by subtracting −9 from −5 (−9 − (−5)), again yielding 4.

Therefore, the correct answers are:

• C) 4 is the distance on the number line.
• D) | −5 − (−9) | is the absolute value representing the distance.
• E) | −9 − (−5) | is also the absolute value representing the distance.

The incorrect options are:

• A) −14, B) −4, and F) 14 because the distance cannot be negative and the positive number should be 4, not 14.