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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![A point P lies on the perpendicular bisector of ABif 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 AB, then PA = PB."
a. Provide a counterexample in taxicab geometry. (Note: In taxicab geometry, PA = PB means dr(P, A) = d7(P, B).) Illustrate your counterexample on grid paper and explain how it is a counterexample.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93507587-8486-4bd1-9be9-7c1c5dc70b2a%2Fb0aded6c-b39b-4fcd-ba96-35c1bc5b9a14%2Fze35yk7_processed.png&w=3840&q=75)
Transcribed Image Text:A point P lies on the perpendicular bisector of ABif 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 AB, then PA = PB."
a. Provide a counterexample in taxicab geometry. (Note: In taxicab geometry, PA = PB means dr(P, A) = d7(P, B).) Illustrate your counterexample on grid paper and explain how it is a counterexample.
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