Exercise · ZW-METRIC-SPACE-001 · ★☆☆ Basic
In \(\mathbb{R}^2\) with the Euclidean distance, what is the distance between \((1,2)\) and \((4,6)\)?
Choose one option.
Show answer
- B. 5
Explanation
Compute \(\sqrt{3^2+4^2}=\sqrt{25}=5\). The value 7 is the taxicab distance and 25 forgets the root.
Review the concept: Metric space
A metric space is a set \(X\) together with a distance \(d\) between its points: a nonnegative number for each pair, symmetric, zero only between a point and itself, and satisfying the triangle inequality.
\[\begin{aligned}d(x,y)&=0\iff x=y,\qquad d(x,y)=d(y,x),\\ d(x,z)&\le d(x,y)+d(y,z)\end{aligned}\]
More practice problems: metric space
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