Now fill in the otherpointsthat involvea combinationof movingup, down,and over.Countthe pointsto find that thereare 12 distinctpointson the circle.TaxicabMidpoints
Muchlike findingtaxicabdistances,you can also identifytaxicabmidpoints.However, unliketraditional
midpoints,theremay be morethan one midpointbetweentwo pointsin taxicabgeometry. To find a taxicab
midpoint,tracea path betweenthe givenpathsalongthe roads,axes,or lines.Then,dividethe distanceby
2 and countthat manyunitsalongyour path.This resultsin identifyinga taxicabmidpoint.As you will see,
theremay be morethan one midpointbetweenany two points.
Example 3
Find the taxicabmidpointsbetween and in the diagrambelow.Startby findingthe taxicabdistance. You will haveto travel6 unitsto the right and 2 unitsup. Add
thesetwo valuesto find the distance.
The taxicabdistance, is 8 units.Use the diagramand identifyhow manypointsare 4 unitsawayfrom
and. Thesewill be the taxicabmidpoints.Thereare threetaxicabmidpointsin this scenario,shownin the diagramabove.