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Find the distance between the following pair of points:
$(a, 0)$ and $(0, b)$
Given:
The given pair of points is $(a, 0)$ and $(0, b)$.
To do:
We have to find the distance between the given pair of points.
Solution:
We know that,
The distance between two points \( \mathrm{A}\left(x_{1}, y_{1}\right) \) and \( \mathrm{B}\left(x_{2}, y_{2}\right) \) is \( \sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \).
Therefore,
The distance between the points $(a, 0)$ and $(0, b)$\( =\sqrt{(0-a)^{2}+(b-0)^{2}} \)\( =\sqrt{(-a)^{2}+(b)^{2}} \)
\( =\sqrt{ a^{2}+ b^{2}} \)
The distance between the given pair of points is $\sqrt{a^2+b^2}$.
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