The Correct Answer and Explanation is:
The correct answer is 16.4 units.
Explanation
Plotting the Points
To begin, we need to locate both -10.2 and 6.2 on the number line. The number line shows integers marked, with zero at the center.
- Plotting -10.2: Negative numbers are located to the left of zero. First, find the mark for -10. The number -10.2 is slightly more negative than -10, so its position will be a very small distance to the left of the -10 mark.
- Plotting 6.2: Positive numbers are located to the right of zero. First, find the mark for the integer 5, and then count one unit to the right to find the mark for 6. The number 6.2 is slightly greater than 6, so its position will be a very small distance to the right of the 6 mark.
Finding the Distance
Distance on a number line represents the total space between two points and is always a positive value. There are two common methods to calculate it.
Method 1: Using Zero as a Reference Point
A simple way to visualize the distance is to calculate each number’s distance from zero and then add them together, since they are on opposite sides of zero.
- The distance from -10.2 to 0 is 10.2 units.
- The distance from 0 to 6.2 is 6.2 units.
To find the total distance between the two points, we add these individual distances:
10.2 + 6.2 = 16.4 units.
Method 2: Using the Distance Formula
The formal way to find the distance between any two points on a number line is to take the absolute value of their difference. The formula is |Point 2 – Point 1|.
Let’s subtract -10.2 from 6.2:
Distance = |6.2 – (-10.2)|
Subtracting a negative number is the same as adding its positive counterpart:
Distance = |6.2 + 10.2|
Distance = |16.4|
The absolute value of 16.4 is simply 16.4. Therefore, the distance between -10.2 and 6.2 is 16.4 units. Both methods confirm the same result.
