Question

The distance between two points, a and b, on a number line is expressed as |a – b|, where a and b are rational numbers. Think about locating a point halfway between a and b on a number line. How can you find the coordinate for such a point? Develop a formula in terms of a and b that you can use to find the coordinate. Your formula must work for positive and negative values of a and b. Does absolute value play a role in your formula? Why or why not? Under what circumstances might your formula be used in the real world? Explain.

Answer 1

Answer:

$d = \frac{1}{2}|a- b|$

Step-by-step explanation:

Given

$D = |a- b|$

Required

Distance of half way a and b

To do this, we simply divide the original distance by 2

i.e.

$d = \frac{1}{2}D$

Substitute $D = |a- b|$

$d = \frac{1}{2}|a- b|$

Since it is an absolute function, then the formula will work fine for all values of a and b. e.g.

$a = 5.4\ b = -2.6$

The distance between a and b is:

$D = |a- b|$

$D = |5.4 - -2.6|$

$D = |8|$

Remove absolute sign

$D = 8$

The halfway point is:

$d = \frac{1}{2}D$

$d = \frac{1}{2} * 8$

$d = 4$

Yes, absolute function play a role in the calculation (this has been stated above). However, the reason is that all negatives will be removed from the end result.

In real world, the formula can be used to calculate the distance between two athletes. Say an athlete is at 200 m mark while another is at 80 m mark.

The half way distance between them is:

$d = \frac{1}{2}|200 - 80|$

$d = \frac{1}{2}|120|$

Remove absolute sign

$d = \frac{1}{2}*120$

$d = 60$