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Mathematics-Online problems:

Interactive Problem 236: Distance between Points in the Maximum Norm

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
What is the form of the set $ D\subset\mathbb{R}^2$, of all points having the same distance from the points $ P=(4,1)$ and $ Q=(7,5)$ with respect to the maximum norm

$\displaystyle \Vert x \Vert _\infty=\max\{\vert x_1\vert, \vert x_2\vert\} \ ?$

\includegraphics[width=4cm]{g76_bild1}
$ D:\quad \Vert x-p\Vert _\infty=\Vert x-q\Vert _\infty$
Find the point $ M$, that has the same distance from $ P$, $ Q$ and $ R=(2,3)$ with respect to $ \Vert\cdot\Vert _\infty$.


Solution:

Form of the set $ D$: no answer,
a line , several segments of lines ,
a square , several squares ,
a circle , several circles .

$ M=($ , $ )$ (declaration in decimals)
   

(Authors: Höllig/Höfert)

see also:

  automatically generated: 8/11/2017