Sheet F (Geometric Structures)

Taxicab Geometry

prepared by:

Joseph Malkevitch
Department of Mathematics and Computing
York College (CUNY)
Jamaica, New York 11451

Email: malkevitch@york.cuny.edu

web page:

http://www.york.cuny.edu/~malk

1. Given the points (0, 0) and (4, 4)

a. Find the euclidean distance between them.

b. Find the taxicab distance between the.

c. Find the points in euclidean plane equidistant from these two points.

d. Find the points in the taxicab plane equidistant from these two points.

2. Given the points (0, 0) and (2, 12)

a. Find the euclidean distance between them.

b. Find the taxicab distance between the.

c. Find the points in euclidean plane equidistant from these two points.

d. Find the points in the taxicab plane equidistant from these two points.
(How can one describe these points using equations?)

3. Given the points (0, 0) and (20, 4)

a. Find the euclidean distance between them.

b. Find the taxicab distance between the.

c. Find the points in euclidean plane equidistant from these two points.

d. Find the points in the taxicab plane equidistant from these two points. (How can one describe these points using equations?)

4. Given the points (2, 10) and (4, 2)

a. Find the euclidean distance between them.

b. Find the taxicab distance between the.

c. Find the points in euclidean plane equidistant from these two points.

d. Find the points in the taxicab plane equidistant from these two points. (How can one describe these points using equations?)

5. Given the points (4, 6) and (12, 2)

a. Find the euclidean distance between them.

b. Find the taxicab distance between the.

c. Find the points in euclidean plane equidistant from these two points.

d. Find the points in the taxicab plane equidistant from these two points. (How can one describe these points using equations?)

6. a. A cab can travel at an average rate of 20 miles per hour. How long will it take to travel between (12, 10) and (30, 20) (numbers given in miles)?

b. How long would it take an animal which which walked at a rate of 4 miles per hour to get between the two points using a "crow flies" path?

7. Are the following two triangles congruent in the taxicab plane?

A = (0, 0), B = (1, 1), and C = (1, 0)

A'= (0, 0), B' = (0, 2), and C' = (1, 1)

Are they congruent in the Euclidean plane?