2. (i) Let L be the set of points on the line-segment between vertices (1,0) and (0, 1). By considering the set of vectors {Ai + (1 - A)j: 0 ≤≤ 1}, show that the maximal distance between the origin and the line-segment L is 1. (ii) Use your result from part (i) to show that for any square with sides of length 1, the maximal distance between any two points on the square is √2. (iii) Show that for any two squares with side-length 1 and a non-empty intersection, the maximal distance between two points within their union is 2√2.

2. (i) Let L be the set of points on the line-segment between vertices (1,0) and (0, 1). By considering the set of vectors {Ai + (1 - A)j: 0 ≤≤ 1}, show that the maximal distance between the origin and the line-segment L is 1. (ii) Use your result from part (i) to show that for any square with sides of length 1, the maximal distance between any two points on the square is √2. (iii) Show that for any two squares with side-length 1 and a non-empty intersection, the maximal distance between two points within their union is 2√2.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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