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 & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 30E
Related questions
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Transcribed Image Text: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.
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