Perpendicular Bisectors & Taxicab Geometry

Perpendicular Bisectors:

There are 2 new theorems for perpendicular bisectors that we learned today in class.

Theorem #1: 2 points equidistant to end points implies perpendicular bisector

An example of this theorem is shown here...

The word equidistant is defined as... The vertex is the same distance away from the 2 endpoints

The 2nd theorem we learned today was...

Theorem 2: A point on a perpendicular bisector implies equidistance from the 2 endpoints

Taxicab Geometry:

Taxicab Geometry can be defined as...a form of geometry in which the usual metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the absolute differences of their coordinates

An example of taxicab geometry is shown here by a taxicab circle:

A taxicab circle is a circle in which all of the surrounding points are equal distance away from the center of the circle, and take the shortest route to that given point.

That's just about all we learned in class today. Thank you.

-Michael Levitsky