Latitude and Longitude:
A Real Life Example of the Distance Formula


Author: Robin A. Ward, California Polytechnic State University-San Luis Obispo


Audience: algebra 1 or algebra 2 students


Mathematical Topics: distance formula, coordinate graphing


Materials:

latitude and longitude coordinates of NASA sites
map of U.S.



The Activity:

  • In the previous activity, some students may have noticed that the shortest distance between any two locations is NOT found by moving along the latitude lines and then along the longitude lines (shown in purple). Instead, the shortest distance between two locations is found by drawing a straight line connecting the two locations (shown in red ).

    PLEASE NOTE: For simplicity sake, let us make the assumption that the world is flat so that we can apply the distance formula to this problem. Certainly, the earth is round! Thus, the distances computed in this activity will not be as exact as if we were considering the curvature of the earth. However, given that the coordinates of latitude and longitude clearly define a specific location, we will use this opportunity to compute the distance between two locations.

  • Ask students the following question: "Using the lines of latitude and longitude, what is the distance (in degrees) if you were to travel from NASA Dryden to NASA Ames?"

  • Based on the map, NASA Dryden is located (approximately) at 117 degrees longitude and 34 degrees latitude. NASA Ames is located (approximately) at 122 degrees longitude and 37 degrees latitude. Students can consider the individual latitude and longitude information for each location as forming a coordinate pair. That is, NASA Dryden is located at (34, 117) and NASA Ames is located at (37, 122).

  • Using this information, students can use the distance formula to find the distance (measured in degrees) between these two locations.

  • Promote a discussion with students as to whether the solution of 5.83 degrees makes sense. Recall that given any right triangle, the hypotenuse measures longer than either of its legs. In this case, the hypotenuse is indeed longer than either of the two legs of the triangle (shown in purple).

    Recall that we are making the assumption that the world is flat so that we can apply the distance formula to this problem. Certainly, the earth is round! Thus, the distances computed in this activity will not be as exact as if we were considering the curvature of the earth. However, given that the coordinates of latitude and longitude clearly define a specific location, we will use this opportunity to compute the distance between two locations.

    Also, notice that travel directly along the hypotenuse is indeed the shortest distance between the two locations. The other alternative would be to travel first along the horizontal leg of the triangle 5 degrees and then move vertically 3 degrees, for a total trip of 8 degrees. Thus, the hypotenuse is the shortest path of travel between NASA Dryden and NASA Ames.

  • Provide students with additional practice using the distance formula by finding the distance (measured in degrees) between other NASA sites.


    Enrichment Activity: Students can continue applying the distance formula, finding the distance between state capitals using a map of U.S. or by using the latitude and longitude coordinates of various other cities.


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    • Funded by the NASA Dryden Flight Research Center


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