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.
Discuss how you can find the coordinate of a point located other fractional distances
from a to b (or from b to a). For example, locate a point three-fourths of the distance
from a to b. What kind of calculation is involved?