What is the distance between $(4, 0)$ $(4,0)$ and $(5, 2)$ $(5,2)$ ?

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What is the distance between $(4, 0)$ $(4,0)$ and $(5, 2)$ $(5,2)$ ?

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Answer 1 · 2016-01-02T22:04:27

$\sqrt{5}$ $sqrt5$

Explanation:

Let's say $A (4, 0)$ $A(4,0)$ and $B (5, 2)$ $B(5,2)$ . The distance between those points is the norm of the vector $A B (x_{b} - x_{a}, y_{b} - y_{a}) = (1, 2)$ $AB(x_b - x_a,y_b - y_a) = (1,2)$ .

The norm of a vector $u (x, y)$ $u(x,y)$ is given by the formula $\sqrt{x^{2} + y^{2}}$ $sqrt(x^2 + y^2)$ .

So the norm of $A B$ $AB$ is $\sqrt{1^{2} + 2^{2}} = \sqrt{5}$ $sqrt(1^2 + 2^2) = sqrt(5)$ which is the distance between $A$ $A$ and $B$ $B$ .

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What is the distance between $(4, 0)$ $(4,0)$ and $(5, 2)$ $(5,2)$ ?

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What is the distance between (4,0) (4,0) (4,0) and (5,2) (5,2) (5,2) ?

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What is the distance between $(4, 0)$ $(4,0)$ and $(5, 2)$ $(5,2)$ ?