Question

The distance between two points, a and b, on a number line is expressed as la – bl. 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

Step-by-step explanation

The distance between two points a dna b on a number line is given as:

|a - b|

Given that point a is greater than point b.

To locate the midpoint between point a and point b, we can use the formula for distance given above.

Because the midpoint is the point that divides a distance (between two points) into two equal halves, then we have to simply find half of the distance.

Because we have to consider possible positive and negative values of a and b, the absolute value cannot play a role in the formula.

This is because absolute value is always positive and that is not always the case for the midpoint of a and b.

Therefore, the midpoint between a and b is:

`M\text{ = }\frac{a\text{ - b}}{2}`

This formula works for both positive and negative values of a and b.

In the real world, we can use the formula to find the midpoint between two positions on a map.