Algebra 1
Name__________
Mathematics using Latitude and Longitude. Finding the
distance between locations.
Algebra 1: distance formula (based on the Pythagorean
Theorem)
d
1.
 x  x
2
  y  y
2
Before using the world coordinates to find the distance between cities we must practice finding the
distance between 2 points plotted on a coordinate plane.
A. Find the distance between Pt A(4, 6) and Point B (-3, -2)
Just like our slope formula: slope  y  y
xx
It doesn’t matter which point we start with but
The order is important!
So plugging (4,6) and (-3,-2) in we get:
d
 x  x
2
  y  y
2
2
2
2
2
2
2
 4  3   6  2  =  4  3   6  2  =  7   8
= 49  64 = 49  64 = 113 = 10.63
d
B. Find the distance between Pt. M (-5,4) and N (7,-3)
d
 x  x
2
  y  y
2
C. We are now going to use the world coordinates you found earlier to calculate the distance between some
cities in the United States (please note there is significant error associated with this formula…we are
using a plane formula – as if the United States is “flat”)
Each City will have coordinates (Lat, Long)
All North and East coordinates are POSITIVE
All South and West coordinates are NEGATIVE
Prime Meridian
(-, +)
(+,+)
Equator
(-, -)
(+,-)
From your notes worksheet you completed earlier today. Fill out the table below but use +, or – in the
appropriate locations. Example: Columbus Ohio has coordinates Latitude 40 N Longitude 83 W so its
coordinates are (40, -83)
Coordinates of :
Columbus OH (40, -83)
Chicago IL _______________
Miami FL ______________
New York NY______________
Houston TX_____________
D. Use the fact that each degree is 70 miles and find the distance from Chicago to Columbus – Show work
i)
Use the distance formula , d   x  x 2   y  y 2 and substitute the appropriate coordinates.
ii)
Then multiply this distance by 70
E. Neatly show all work and find the distance, in miles, from Miami to Columbus:
F. Neatly show all work and find the distance, in miles, from New York City to Columbus:
G. Neatly show all work and find the distance, in miles, from Houston to Columbus:
Algebra 1 Requirement
Your group is investigating a certain country or culture. Your trifold board must include some form of a map
indicating where the “focus city” of your country or culture is located.
Your trifold board must also list the Geographic Coordinates of this city.
You will list these as Latitude________________ N or S, Longitude ____________ E or W
Your group will do this by
entering the coordinates of Columbus, Ohio and the focus city of your country into the
website: http://jan.ucc.nau.edu/~cvm/latlongdist.html
You must then find the distance, in miles, from this city to Columbus, Ohio.
We cannot use our distance formula to calculate the distance – our distance formula works for a plane (flat)
object.
You must enter the coordinates as: ddd.ffffD
where ddd = 0-3 digits, ffff = 0-10 digits and D = N,S,E, or W. This format represents a decimal
number of degrees. If the number of degrees is a whole number, the decimal point is optional.
For Example, Columbus Ohio will be entered as your source city and would be entered as:
Source
Latitude :
40.0N
Longitude:
83.0W
Destination
Latitude :
Longitude:
After entering the coordinates of your city in the “destination” section, leave the units in statute miles and
submit your query.