To determine the distance between points -57 and 13 on a number line, we need to calculate the absolute difference between these two points.
Let's go through the step-by-step process:
1. Identify the two points on the number line:
- Point 1: -57
- Point 2: 13
2. Calculate the difference between the points:
- The difference between -57 and 13 is calculated by subtracting one point from the other. We can do this in two ways:
1. [tex]\( 13 - (-57) \)[/tex]
2. [tex]\( -57 - 13 \)[/tex]
3. Simplify the subtraction:
- For the first method:
[tex]\( 13 - (-57) = 13 + 57 = 70 \)[/tex]
- For the second method:
[tex]\( -57 - 13 = -70 \)[/tex]
4. Take the absolute value:
- The distance on a number line is always a positive value. Thus, regardless of the direction, the absolute difference is taken:
- [tex]\( |13 - (-57)| = |70| = 70 \)[/tex] for the first method
- [tex]\( |-57 - 13| = |-70| = 70 \)[/tex] for the second method
5. Conclusion:
- The distance between -57 and 13 on the number line is 70.
Therefore, the correct answer is [tex]\( \boxed{70} \)[/tex].
