Question

The distance between two points, a and b, on a number line is expressed as

Answer 1

The distance between points (a) and (b) is the number of units between the points.

Formula for halfway two

Assume the lesser point is point (a)

To locate the halfway between points (a) and (b)

• Calculate the absolute difference between points (a) and (b) i.e. |a - b|
• Divide the difference into halves
• Add the value of one half to point (a).

The above steps is represented as:

$P = a + \frac{|a - b|}{2}$

Using the above formula, the halfway point between 5 and 11 would be 8

The formula can be used to calculate the distance between negative points, and absolute values are used to determine the number of units between the points

Real world circumstance

The formula can be used to calculate the halfway distance between two points on a track

Fractional distance

To determine the fractional distance, we simply replace the 1/2 in the original formula with the appropriate fraction.

Take for instance, three-fourths from (a) to (b) would be:

$P = a + \frac{3|a - b|}{4}$

Read more about distance at:

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