What is the distance between -34 and 16
The Correct Answer and Explanation is :
To find the distance between (-34) and (16) on a number line, we can use the concept of absolute distance between two points. The formula for the distance between two points, (a) and (b), on a number line is:
[
\text{Distance} = |a – b|
]
In this case, (a = -34) and (b = 16). So:
[
\text{Distance} = |-34 – 16|
]
Now, calculate inside the absolute value:
[
-34 – 16 = -50
]
Then take the absolute value:
[
|-50| = 50
]
Thus, the distance between (-34) and (16) is (50).
Explanation:
This problem requires understanding the concept of absolute value and distance on a number line. When calculating distance, we’re looking at how far two numbers are from each other, without considering direction. The absolute value function, denoted by vertical bars (| \cdot |), transforms any negative number into a positive one, which is useful here because distance cannot be negative.
In terms of visualization, imagine a number line where (-34) is on the left side and (16) is on the right. To calculate the distance between them, you start from (-34) and move rightward until you reach (16). Counting each unit would indeed give you a distance of (50) units.
This calculation can also be understood by breaking it down into parts: from (-34) to (0) is (34) units, and from (0) to (16) is another (16) units. Adding these two distances:
[
34 + 16 = 50
]
This confirms that the distance is indeed (50), no matter the method used.