Superlesson
Project 6-1
Algebra
Chapter 6
Systems of Equations and Inequalities
The triangulation process is used in many occupations. Cartographers use it while making maps; firefighters use it to pin point of forest fires. You can use information from the World Wide Web to plot triangulation points.
Part B, Systems of Linear Equations
1. Look at the Map of Paris Web site that shows the city's museums and monuments. Print the map and use it with an overhead transparency of 1 cm graph paper to complete the following problems. Make a coordinate axis on your graph paper.
a. If the Musée des Arts Decoratifs is the origin, what is the equation of the line containing Musée de l'Orangerie and Musée Auguste Rodin?
b. If the Musée des Arts Decoratifs is the origin, what is the equation of the line containing the monuments Conciergerie and Place Vendome?
c. What is the relationship between the lines containing these points? Explain. Where do the lines intersect?
Part C, Making Connections
2. Using your map from 1, plan a path from the Tour Eiffel along a line with a slope of 2/3. What monument or museum would you encounter? Explain your reasoning.
3. What would be the slope of the line containing the Musée des Arts Decoratifs and the Cité des Science et de l'Industrie?
4. Using a pencil of a second color, draw a perpendicular
line to the line described in 2. If the origin is at #2,
what monument is on this perpendicular line? What are the coordinates
if your graph is in centimeters?