Question
========

Given two points $p = (2, 4)$ and
$q = (4, 4)$ in a Cartesian coordinate system:

Questionlist
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* What is the Manhattan distance $d_1(p, q)$?
* What is the Euclidean distance $d_2(p, q)$?
* What is the maximum distance $d_\infty(p, q)$?


Solution
========

The distances are visualized below in green ($d_1$), red ($d_2$),
and blue ($d_\infty$).

![](dist-1.svg)

Solutionlist
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* $d_1(p, q) = \sum_i |p_i - q_i| = |2 - 4| +
  |4 - 4| = 2$.
* $d_2(p, q) = \sqrt{\sum_i (p_i - q_i)^2} = \sqrt{(2 -
  4)^2 + (4 - 4)^2} = 2$.
* $d_\infty(p, q) = \max_i |p_i - q_i| = \max(|2 -
  4|, |4 - 4|) = 2$.


Meta-information
================
extype: cloze
exsolution: 2|2|2
exclozetype: num|num|num
exname: Distances
extol: 0.01