School Districts (2017)

Prepared by:

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

email:

malkevitch@york.cuny.edu

web page:

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

A town is laid out strictly using square blocks (Figure 1).

Figure 1 (Portion of a town laid out in a grid.)

One can introduce coordinates for the "vertices" of the town (which we assume goes off to "infinity" in all directions) by labeling the points of the grid with ordered pairs of integers (x,y). Thus, if the point at the lower left hand corner in Figure 1 is labeled (0, 0), then the upper right hand corner would get the label (5, 3). Suppose that Madison School is located at (-6, -1), Monroe School is located at (2,1) and Adams School is located (-3, -3). If students go to the school which they are closest to as measured using taxicab distance (e.g. the distance from (-2, 1) to (3, 4) is 8), determine the points that lie in the school district for each of the schools.

Hint: Which points are equidistant from Madison School and Adams School? Which points are equidistant from Madison School and Monroe School? Which points are equidistant from Monroe and Adams School? (Use taxicab distance.)