Name:
______
Name:
______
Name:
______
Name:
______
What’s the Distance??
1. Refer to the map of Colorado above. Discuss with your group all of the different ways you could travel from
Rifle, Colorado to Lamar, Colorado.
a. If you were driving in a car and all of the axis lines were roads, find 5 different paths you could take
to drive from Rifle to Lamar without backtracking (traveling only East and South)?
b. (Each unit on the map is equal to 40mi.) What is the total distance south that you’ll drive for each
path? What is the total distance east that you’ll drive for each path? Are those distances same for all
of the paths you found? What is the total distance from Rifle to Lamar?
c. What if you were in an airplane and you didn’t have to worry about roads? What would be the
quickest path to get from Rifle to Lamar?
2. When you’re driving along the roads you could find the distance by counting the number of units between
Rifle and Lamar. How could you find the distance between the two cities if you’re traveling by airplane?
(Hint: What shape could you draw by connecting the two cities? What formula would you use?)
3. Use your answer for question 2 to create a general formula you could use to find the distance between two
points. (Was there a particular theorem you may have used to answer question 2?)
d=
At this time we will come together as a class and discuss what you’ve found. I will ask each group do share
their strategies for finding their formula.
For Questions #4-5, use the formula we agreed on as a class for Question #3
4. Find the distance between the points (7, -2) and (-2, 3).
5. Find the distance between the points (-3, -1) and (6, 10).
6. What if you’re plane ran out of fuel when you were exactly halfway between Rifle and Lamar? Discuss with
your group how you could find the point that lies EXACLY halfway between the two cities.
7. What city is the closest to the halfway point between Rifle and Lamar? Explain the strategy that your group
used to find that point.