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Consider the statement "If P is a point on the perpendicular bisector of segment AB, then PA= PB: a. Provide a counterexample in taxicab geometry. (Note: In taxicab geometry, PA= PB means d7(P, A) = dr(P, B).) Illustrate your counterexample on grid paper and explain how it is a counterexample.

Consider the statement "If P is a point on the perpendicular bisector of segment AB, then PA= PB: a. Provide a counterexample in taxicab geometry. (Note: In taxicab geometry, PA= PB means d7(P, A) = dr(P, B).) Illustrate your counterexample on grid paper and explain how it is a counterexample.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**A point \( P \) lies on the perpendicular bisector of \( \overline{AB} \) if and only if \( PA = PB \).** Analyze what goes wrong with this theorem in taxicab geometry by completing the following two problems: 1. Consider the statement "If \( P \) is a point on the perpendicular bisector of segment \( \overline{AB} \), then \( PA = PB \)." a. Provide a counterexample in taxicab geometry. (Note: In taxicab geometry, \( PA = PB \) means \( d_T(P, A) = d_T(P, B) \).) Illustrate your counterexample on grid paper and explain how it is a counterexample.
Transcribed Image Text:**A point \( P \) lies on the perpendicular bisector of \( \overline{AB} \) if and only if \( PA = PB \).** Analyze what goes wrong with this theorem in taxicab geometry by completing the following two problems: 1. Consider the statement "If \( P \) is a point on the perpendicular bisector of segment \( \overline{AB} \), then \( PA = PB \)." a. Provide a counterexample in taxicab geometry. (Note: In taxicab geometry, \( PA = PB \) means \( d_T(P, A) = d_T(P, B) \).) Illustrate your counterexample on grid paper and explain how it is a counterexample.
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