2. Consider R² with the usual definition of lines, but with distance function d = [√(x2-x1) + √(y2-y₁)1². Show that the triangle inequality is not true in this geometry by finding a triangle ABC such that AB + BC < AC.3. Prove that if P, Q, and R are three points on a line, then exactly one of the points is between the other two. (This can be done using a coordinate system on the line.)

Answered: Image /qna-images/answer/e7ef412e-d871-42cc-9d35-4bbf3c375307.jpg

2. Consider R² with the usual definition of lines, but with distance function d = [√(x2-x₁) + √(2-₁)]². Show that the triangle inequality is not true in this geometry by finding a triangle ABC such that AB + BC < AC.

2. Consider R² with the usual definition of lines, but with distance function d = [√(x2-x₁) + √(2-₁)]². Show that the triangle inequality is not true in this geometry by finding a triangle ABC such that AB + BC < AC.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter1: Line And Angle Relationships

Section1.4: Relationships: Perpendicular Lines

Problem 27E

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Question

2. Consider R² with the usual definition of lines, but with distance function d = [√(x2-x1) + √(y2-y₁)1². Show that the triangle inequality is not true in this geometry by finding a triangle ABC such that AB + BC < AC.
3. Prove that if P, Q, and R are three points on a line, then exactly one of the points is between the other two. (This can be done using a coordinate system on the line.)

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