Applied Math 20S - Coordinate Geometry Project
The Task
The Mountain View School Division is looking at constructing towers that will allow all its schools to connect to the Internet by high-speed DSL connection. This will also allow the schools to communicate among each other. You job is to use coordinate geometry to determine the best locations for the towers. You may work with a partner or by yourself.
Background
Wireless transmission requires the use of transmitting and receiving towers. If the transmission is over long distance a repeater tower may be used in between the two sites to 'boost' the signal. The best location for these repeater towers is at the midpoint between the two sites.
A) Background Questions
Go to site http://plantwatch.sunsite.ualberta.ca/determineloc.php Answer these questions
1.
What are latitude & longitude? Which way do each run? Draw a picture to illustrate. (3)
2.
How are lines of latitude and longitude divided? (2)
3.
How close can you locate an object using only minutes of a degree? How close do you think you can get by using seconds? Show work to justify your answer. (2)
4.
How far apart are lines of latitude? (1)

5.
What line of longitude through Greenwich, England? (BONUS: (1) What is the name?) (1)
6.
How far apart are lines of longitude in Manitoba? Is this the same all over the world? (2)
7.
What is the latitude (in degrees, minutes and seconds) for The University of
Alberta Devonian Botanic Garden? Show how this location can be converted into decimal form. (2)

B) Getting Started
1.
Determine all towns in the Mountain View school division. Use the division website http://www.mnview.org to list them all.
2.
Use the website http://geonames.nrcan.gc.ca/search/search_e.php
to determine the locations of all towns in Mountain View School Division. Click on
INFO to find the latitude and longitude. Do not use the section, township & range.
Be sure you find the town or city (not a lake or river) and that it is in Manitoba.
Record these using degrees, minutes and seconds.
3.
Convert all these locations to decimal form.
4.
Fill in the spreadsheet that lists the towns, their longitudes and latitudes in decimal form. (6) town longitude latitude Decimal Longitude Decimal Latitude
5.
Create a scatter plot of this data that results in a type of 'map' of the division.
Label all towns. (4) NOTE: Longitude is the X coordinate .
OR
Create a pencil and paper graph (map) showing the locations of the towns.
NOTE: DO NOT start your scales at zero. Make the graph as big as possible.

C) Project Presentation
Big Valley School Division is an imaginary school division. It has 7 towns with the following coordinates. It would like to build a similar wireless network to Mountain
View's network. It will use the town of BRANDEN as a centre hub that all other towns will connect to.
Town
Albertville
BRANDEN
Cowtown
Darlingford
Elephant Rock
Longitude Latitude
47.5 32
48.9
50
30.7
37.9
51.1
53.1
25.6
31
Fairford 46.8 24.8
Goola Goola 48.7 37.8
1) Use a spreadsheet or pencil and paper to create a scatter plot of the division. Label all towns. (4)
2) Using the distance formula, determine the distance between all the towns and
BRANDEN. (3)

3) If the distance between BRANDEN and a town is greater than 5, determine the midpoint between the towns. Show how you did this. Each midpoint will require a booster tower to boost the signal. Plot the midpoints on the graph. (2)
4) Are there any midpoints that are within 1 distance unit of each other? If there are, one tower maybe used in place of separate towers. Show work. (2)

5) Determine the total of wireless towers required to service the division. (2)
6) The school at BRANDEN requires a tower that receives signals in all directions.
Determine the total cost of the network. The cost per tower are: (2)
Main, all direction tower - $1000
School smaller tower - $500
Booster tower - $750
BONUS: Explain why we could not have done the Project Presentation with the actual Mountain View locations, but had to make up a imaginary division with made up locations. (2)