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Name: _______________________
Date:_________________________
Can Taxicab Geometry Really Help You Buy a House??
1. In Euclidean Geometry, we define a perpendicular bisector to be the set of all points
that are equal distance from the endpoints of a given segment. The definition is the same
for Taxicab Geometry; however, a Taxicab perpendicular bisector looks different than a
Euclidean perpendicular bisector. Given two points, A ( 1, 1) B (6, 4) graph the Taxicab
perpendicular bisector.
2. Mr. and Mrs. Singletary are moving to Athens so that Mrs. Singletary can attend UGA.
Mr. Singletary gets a job at Winder Barrow High School teaching delightful students
geometrical concepts. They want to choose a home so that the total combined distance
they drive to work is as small as possible. Use the map below to determine where they
should look for a house. Graph your solution.
3. Mr. and Mrs. Singletary have decided that they need to be more fair. They have
decided to look for a house where they not only had a combined minimum distance to
drive to the place of their employment, but also they want each of their drives to work to
be the same distance. Graph your solution.
4. Mrs. Singletary is picky, and is unable to find her dream home in the previous area
designated for their house hunt. So, Mr. Singletary volunteers to drive up to twice as far
to work as his wife, while still minimizing their combined distance. What possibilities
would this allow for their house hunt? Graph your solution.
5. Athens has decided to install an underground subway system. Using the subway helps
to decrease certain walking distance. For example, if Mr. Singletary is at the post office
and wants to go to Krispy Kreme, he walks three blocks south, rides the subway, the
walks two blocks to Krispy Kreme. However, if he was at the library and wanted to go
to Krispy Kreme, there would be no reason to get on the subway because it would be a
longer distance. We shall name this new type of DM , thus DM (P, K) = 5, and DM =(L,
K)=4. (M= Mass Transit)
a) Compute DM from (0, 0) to Krispy Kreme
b) Compute DM from (-6, 2) to Krispy Kreme
c) Compute DM from (6, 4) to Krispy Kreme
d) Sketch the set of all points at mass-transit distance 4 from the point Krispy Kreme.
6. A new cell phone company has arrived in town. They would like to disperse their cell
phone towers in such a way that the fewest number of towers serve the maximum number
of people. Consider each block to be a half mile in distance, and the cell phone towers’
range is approximately 1.5 miles. Develop your plan on a graph for where the cell phone
towers should be placed, and be careful to consider what type of geometry you should use
for your calculations.