How do you find the distance between two points on a number line?

A slow way to calculate the distance between numbers on a number line is to count every number between them. A simpler, faster way is to find the distance through subtraction and absolute values. An absolute value is the positive representation for a number and is symbolized as |a|. For example, the absolute values of 3 and -3, or |3| and |-3|, are both 3. This method of number line distance works for numbers close together and far apart.

Select two numbers on the number line. For this example, the numbers are -9 and 5.

Subtract one number on the number line from the other number. For this example, -9 subtracted from 5 is 14. If subtracting 5 from -9, the answer would be -14.

Obtain the absolute value of the number line difference. For this example, the absolute value for either 14 or -14 -- that is, |14| or |-14| -- is 14. The distance between the two numbers is 14.

2 Answers By Expert Tutors

The distance formula for two points P1: (x1,y1) and P2:  (x2,y2) is:

d = √( (x2-x1)2 + (y2-y1)2 )

On the number line a and b are the x-coordinates and the y-coordinates are both 0.  The points are  (a,0) and (b,0).

In the Distance Formula, this makes the distance:

d = √( (x2-x1)2 )

Now, since the square root may have either both positive and negative roots, we write the value as:

d = ± (x2-x1)

This is either (x2-x1)  or (-(x2 - x1))

When considering distance (a measurement without a sign attached), we write the positive distance:  |x2 - x1|.

To determine distance the starting point is subtracted from the ending point.

iE.g., if you go from 2 to 8 the distance is 8 - 2 or 6. If you go from 8 to 2 the distance is still 6 although 2 - 8 = -6.